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die Fläche nicht als Graph, sondern als Niveaufläche ",[568,2117,2119,2154],{"className":2118},[571],[568,2120,2122],{"className":2121},[575],[577,2123,2124],{"xmlns":579},[581,2125,2126,2151],{},[584,2127,2128,2131,2133,2135,2137,2139,2141,2144,2146,2148],{},[587,2129,2130],{},"F",[591,2132,594],{"stretchy":593},[587,2134,597],{},[591,2136,601],{"separator":600},[587,2138,604],{},[591,2140,601],{"separator":600},[587,2142,2143],{},"z",[591,2145,607],{"stretchy":593},[591,2147,1521],{},[587,2149,2150],{},"c",[609,2152,2153],{"encoding":611},"F(x, y, z) = c",[568,2155,2157,2204],{"className":2156,"ariaHidden":600},[616],[568,2158,2160,2163,2167,2170,2173,2176,2179,2182,2185,2188,2192,2195,2198,2201],{"className":2159},[620],[568,2161],{"className":2162,"style":625},[624],[568,2164,2130],{"className":2165,"style":2166},[629,630],"margin-right:0.1389em;",[568,2168,594],{"className":2169},[635],[568,2171,597],{"className":2172},[629,630],[568,2174,601],{"className":2175},[642],[568,2177],{"className":2178,"style":647},[646],[568,2180,604],{"className":2181,"style":651},[629,630],[568,2183,601],{"className":2184},[642],[568,2186],{"className":2187,"style":647},[646],[568,2189,2143],{"className":2190,"style":2191},[629,630],"margin-right:0.044em;",[568,2193,607],{"className":2194},[655],[568,2196],{"className":2197,"style":1682},[646],[568,2199,1521],{"className":2200},[1686],[568,2202],{"className":2203,"style":1682},[646],[568,2205,2207,2210],{"className":2206},[620],[568,2208],{"className":2209,"style":1309},[624],[568,2211,2150],{"className":2212},[629,630]," gegeben, ist ",[568,2215,2217,2245],{"className":2216},[571],[568,2218,2220],{"className":2219},[575],[577,2221,2222],{"xmlns":579},[581,2223,2224,2242],{},[584,2225,2226,2230,2232,2234,2240],{},[587,2227,2229],{"mathvariant":2228},"normal","∇",[587,2231,2130],{},[591,2233,594],{"stretchy":593},[1511,2235,2236,2238],{"accent":600},[587,2237,564],{},[591,2239,1518],{},[591,2241,607],{"stretchy":593},[609,2243,2244],{"encoding":611},"\\nabla F(\\vec p)",[568,2246,2248],{"className":2247,"ariaHidden":600},[616],[568,2249,2251,2254,2257,2260,2263,2311],{"className":2250},[620],[568,2252],{"className":2253,"style":625},[624],[568,2255,2229],{"className":2256},[629],[568,2258,2130],{"className":2259,"style":2166},[629,630],[568,2261,594],{"className":2262},[635],[568,2264,2266],{"className":2265},[629,1631],[568,2267,2269,2302],{"className":2268},[748,749],[568,2270,2272,2299],{"className":2271},[753],[568,2273,2275,2283],{"className":2274,"style":1627},[757],[568,2276,2277,2280],{"style":1643},[568,2278],{"className":2279,"style":1647},[765],[568,2281,564],{"className":2282},[629,630],[568,2284,2285,2288],{"style":1643},[568,2286],{"className":2287,"style":1647},[765],[568,2289,2292],{"className":2290,"style":2291},[1659],"left:-0.1522em;",[568,2293,2295],{"className":2294,"style":1665},[1664],[1667,2296,2297],{"xmlns":1669,"width":1670,"height":1671,"style":1672,"viewBox":1673,"preserveAspectRatio":1674},[1676,2298],{"d":1678},[568,2300,781],{"className":2301},[780],[568,2303,2305],{"className":2304},[753],[568,2306,2309],{"className":2307,"style":2308},[757],"height:0.1944em;",[568,2310],{},[568,2312,607],{"className":2313},[655]," ein Normalenvektor, und die Tangentialebene lautet ",[568,2316,2318,2369],{"className":2317},[571],[568,2319,2321],{"className":2320},[575],[577,2322,2323],{"xmlns":579},[581,2324,2325,2366],{},[584,2326,2327,2329,2331,2333,2339,2341,2344,2346,2352,2354,2360,2362,2364],{},[587,2328,2229],{"mathvariant":2228},[587,2330,2130],{},[591,2332,594],{"stretchy":593},[1511,2334,2335,2337],{"accent":600},[587,2336,564],{},[591,2338,1518],{},[591,2340,607],{"stretchy":593},[591,2342,2343],{},"⋅",[591,2345,594],{"stretchy":593},[1511,2347,2348,2350],{"accent":600},[587,2349,597],{},[591,2351,1518],{},[591,2353,1609],{},[1511,2355,2356,2358],{"accent":600},[587,2357,564],{},[591,2359,1518],{},[591,2361,607],{"stretchy":593},[591,2363,1521],{},[707,2365,709],{},[609,2367,2368],{"encoding":611},"\\nabla F(\\vec p) \\cdot (\\vec x - \\vec p) = 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(vorausgesetzt ",[568,2577,2579,2614],{"className":2578},[571],[568,2580,2582],{"className":2581},[575],[577,2583,2584],{"xmlns":579},[581,2585,2586,2611],{},[584,2587,2588,2590,2592,2594,2600,2602,2605],{},[587,2589,2229],{"mathvariant":2228},[587,2591,2130],{},[591,2593,594],{"stretchy":593},[1511,2595,2596,2598],{"accent":600},[587,2597,564],{},[591,2599,1518],{},[591,2601,607],{"stretchy":593},[591,2603,2604],{"mathvariant":2228},"≠",[1511,2606,2607,2609],{"accent":600},[707,2608,709],{},[591,2610,1518],{},[609,2612,2613],{"encoding":611},"\\nabla F(\\vec p) \\neq \\vec 0",[568,2615,2617,2730],{"className":2616,"ariaHidden":600},[616],[568,2618,2620,2623,2626,2629,2632,2678,2681,2684,2727],{"className":2619},[620],[568,2621],{"className":2622,"style":625},[624],[568,2624,2229],{"className":2625},[629],[568,2627,2130],{"className":2628,"style":2166},[629,630],[568,2630,594],{"className":2631},[635],[568,2633,2635],{"className":2634},[629,1631],[568,2636,2638,2670],{"className":2637},[748,749],[568,2639,2641,2667],{"className":2640},[753],[568,2642,2644,2652],{"className":2643,"style":1627},[757],[568,2645,2646,2649],{"style":1643},[568,2647],{"className":2648,"style":1647},[765],[568,2650,564],{"className":2651},[629,630],[568,2653,2654,2657],{"style":1643},[568,2655],{"className":2656,"style":1647},[765],[568,2658,2660],{"className":2659,"style":2291},[1659],[568,2661,2663],{"className":2662,"style":1665},[1664],[1667,2664,2665],{"xmlns":1669,"width":1670,"height":1671,"style":1672,"viewBox":1673,"preserveAspectRatio":1674},[1676,2666],{"d":1678},[568,2668,781],{"className":2669},[780],[568,2671,2673],{"className":2672},[753],[568,2674,2676],{"className":2675,"style":2308},[757],[568,2677],{},[568,2679,607],{"className":2680},[655],[568,2682],{"className":2683,"style":1682},[646],[568,2685,2687,2720,2724],{"className":2686},[1686],[568,2688,2690],{"className":2689},[1686],[568,2691,2694],{"className":2692},[629,2693],"vbox",[568,2695,2698],{"className":2696},[2697],"thinbox",[568,2699,2702,2705,2716],{"className":2700},[2701],"rlap",[568,2703],{"className":2704,"style":682},[624],[568,2706,2709],{"className":2707},[2708],"inner",[568,2710,2712],{"className":2711},[629],[568,2713,2715],{"className":2714},[1686],"",[568,2717],{"className":2718},[2719],"fix",[568,2721],{"className":2722},[646,2723],"nobreak",[568,2725,1521],{"className":2726},[1686],[568,2728],{"className":2729,"style":1682},[646],[568,2731,2733,2737],{"className":2732},[620],[568,2734],{"className":2735,"style":2736},[624],"height:0.9274em;",[568,2738,2740],{"className":2739},[629,1631],[568,2741,2743],{"className":2742},[748],[568,2744,2746],{"className":2745},[753],[568,2747,2749,2757],{"className":2748,"style":2736},[757],[568,2750,2751,2754],{"style":1643},[568,2752],{"className":2753,"style":1647},[765],[568,2755,709],{"className":2756},[629],[568,2758,2760,2763],{"style":2759},"top:-3.2134em;",[568,2761],{"className":2762,"style":1647},[765],[568,2764,2766],{"className":2765,"style":1660},[1659],[568,2767,2769],{"className":2768,"style":1665},[1664],[1667,2770,2771],{"xmlns":1669,"width":1670,"height":1671,"style":1672,"viewBox":1673,"preserveAspectRatio":1674},[1676,2772],{"d":1678},").",[559,2775,2777],{"id":2776},"beispiele","Beispiele",[564,2779,2780,2781,686,2949,3001,3002,3082,3083,3202,3203,3324],{},"Für ",[568,2782,2784,2827],{"className":2783},[571],[568,2785,2787],{"className":2786},[575],[577,2788,2789],{"xmlns":579},[581,2790,2791,2824],{},[584,2792,2793,2795,2797,2799,2801,2803,2805,2807,2815,2818],{},[587,2794,589],{},[591,2796,594],{"stretchy":593},[587,2798,597],{},[591,2800,601],{"separator":600},[587,2802,604],{},[591,2804,607],{"stretchy":593},[591,2806,1521],{},[2808,2809,2810,2812],"msup",{},[587,2811,597],{},[707,2813,2814],{},"2",[591,2816,2817],{},"+",[2808,2819,2820,2822],{},[587,2821,604],{},[707,2823,2814],{},[609,2825,2826],{"encoding":611},"f(x, y) = x^2 + y^2",[568,2828,2830,2866,2913],{"className":2829,"ariaHidden":600},[616],[568,2831,2833,2836,2839,2842,2845,2848,2851,2854,2857,2860,2863],{"className":2832},[620],[568,2834],{"className":2835,"style":625},[624],[568,2837,589],{"className":2838,"style":631},[629,630],[568,2840,594],{"className":2841},[635],[568,2843,597],{"className":2844},[629,630],[568,2846,601],{"className":2847},[642],[568,2849],{"className":2850,"style":647},[646],[568,2852,604],{"className":2853,"style":651},[629,630],[568,2855,607],{"className":2856},[655],[568,2858],{"className":2859,"style":1682},[646],[568,2861,1521],{"className":2862},[1686],[568,2864],{"className":2865,"style":1682},[646],[568,2867,2869,2873,2904,2907,2910],{"className":2868},[620],[568,2870],{"className":2871,"style":2872},[624],"height:0.8974em;vertical-align:-0.0833em;",[568,2874,2876,2879],{"className":2875},[629],[568,2877,597],{"className":2878},[629,630],[568,2880,2882],{"className":2881},[744],[568,2883,2885],{"className":2884},[748],[568,2886,2888],{"className":2887},[753],[568,2889,2892],{"className":2890,"style":2891},[757],"height:0.8141em;",[568,2893,2895,2898],{"style":2894},"top:-3.063em;margin-right:0.05em;",[568,2896],{"className":2897,"style":766},[765],[568,2899,2901],{"className":2900},[770,771,772,773],[568,2902,2814],{"className":2903},[629,773],[568,2905],{"className":2906,"style":2439},[646],[568,2908,2817],{"className":2909},[2443],[568,2911],{"className":2912,"style":2439},[646],[568,2914,2916,2920],{"className":2915},[620],[568,2917],{"className":2918,"style":2919},[624],"height:1.0085em;vertical-align:-0.1944em;",[568,2921,2923,2926],{"className":2922},[629],[568,2924,604],{"className":2925,"style":651},[629,630],[568,2927,2929],{"className":2928},[744],[568,2930,2932],{"className":2931},[748],[568,2933,2935],{"className":2934},[753],[568,2936,2938],{"className":2937,"style":2891},[757],[568,2939,2940,2943],{"style":2894},[568,2941],{"className":2942,"style":766},[765],[568,2944,2946],{"className":2945},[770,771,772,773],[568,2947,2814],{"className":2948},[629,773],[568,2950,2952,2974],{"className":2951},[571],[568,2953,2955],{"className":2954},[575],[577,2956,2957],{"xmlns":579},[581,2958,2959,2971],{},[584,2960,2961,2963,2965,2967,2969],{},[591,2962,594],{"stretchy":593},[707,2964,1612],{},[591,2966,601],{"separator":600},[707,2968,2814],{},[591,2970,607],{"stretchy":593},[609,2972,2973],{"encoding":611},"(1, 2)",[568,2975,2977],{"className":2976,"ariaHidden":600},[616],[568,2978,2980,2983,2986,2989,2992,2995,2998],{"className":2979},[620],[568,2981],{"className":2982,"style":625},[624],[568,2984,594],{"className":2985},[635],[568,2987,1612],{"className":2988},[629],[568,2990,601],{"className":2991},[642],[568,2993],{"className":2994,"style":647},[646],[568,2996,2814],{"className":2997},[629],[568,2999,607],{"className":3000},[655]," ist ",[568,3003,3005,3034],{"className":3004},[571],[568,3006,3008],{"className":3007},[575],[577,3009,3010],{"xmlns":579},[581,3011,3012,3031],{},[584,3013,3014,3016,3018,3020,3022,3024,3026,3028],{},[587,3015,589],{},[591,3017,594],{"stretchy":593},[707,3019,1612],{},[591,3021,601],{"separator":600},[707,3023,2814],{},[591,3025,607],{"stretchy":593},[591,3027,1521],{},[707,3029,3030],{},"5",[609,3032,3033],{"encoding":611},"f(1, 2) = 5",[568,3035,3037,3073],{"className":3036,"ariaHidden":600},[616],[568,3038,3040,3043,3046,3049,3052,3055,3058,3061,3064,3067,3070],{"className":3039},[620],[568,3041],{"className":3042,"style":625},[624],[568,3044,589],{"className":3045,"style":631},[629,630],[568,3047,594],{"className":3048},[635],[568,3050,1612],{"className":3051},[629],[568,3053,601],{"className":3054},[642],[568,3056],{"className":3057,"style":647},[646],[568,3059,2814],{"className":3060},[629],[568,3062,607],{"className":3063},[655],[568,3065],{"className":3066,"style":1682},[646],[568,3068,1521],{"className":3069},[1686],[568,3071],{"className":3072,"style":1682},[646],[568,3074,3076,3079],{"className":3075},[620],[568,3077],{"className":3078,"style":2571},[624],[568,3080,3030],{"className":3081},[629],", ",[568,3084,3086,3114],{"className":3085},[571],[568,3087,3089],{"className":3088},[575],[577,3090,3091],{"xmlns":579},[581,3092,3093,3111],{},[584,3094,3095,3101,3103,3105,3107,3109],{},[702,3096,3097,3099],{},[587,3098,589],{},[587,3100,597],{},[591,3102,1521],{},[707,3104,2814],{},[587,3106,597],{},[591,3108,1521],{},[707,3110,2814],{},[609,3112,3113],{"encoding":611},"f_x = 2x = 2",[568,3115,3117,3172,3193],{"className":3116,"ariaHidden":600},[616],[568,3118,3120,3123,3163,3166,3169],{"className":3119},[620],[568,3121],{"className":3122,"style":682},[624],[568,3124,3126,3129],{"className":3125},[629],[568,3127,589],{"className":3128,"style":631},[629,630],[568,3130,3132],{"className":3131},[744],[568,3133,3135,3155],{"className":3134},[748,749],[568,3136,3138,3152],{"className":3137},[753],[568,3139,3141],{"className":3140,"style":1362},[757],[568,3142,3143,3146],{"style":1365},[568,3144],{"className":3145,"style":766},[765],[568,3147,3149],{"className":3148},[770,771,772,773],[568,3150,597],{"className":3151},[629,630,773],[568,3153,781],{"className":3154},[780],[568,3156,3158],{"className":3157},[753],[568,3159,3161],{"className":3160,"style":788},[757],[568,3162],{},[568,3164],{"className":3165,"style":1682},[646],[568,3167,1521],{"className":3168},[1686],[568,3170],{"className":3171,"style":1682},[646],[568,3173,3175,3178,3181,3184,3187,3190],{"className":3174},[620],[568,3176],{"className":3177,"style":2571},[624],[568,3179,2814],{"className":3180},[629],[568,3182,597],{"className":3183},[629,630],[568,3185],{"className":3186,"style":1682},[646],[568,3188,1521],{"className":3189},[1686],[568,3191],{"className":3192,"style":1682},[646],[568,3194,3196,3199],{"className":3195},[620],[568,3197],{"className":3198,"style":2571},[624],[568,3200,2814],{"className":3201},[629]," und ",[568,3204,3206,3235],{"className":3205},[571],[568,3207,3209],{"className":3208},[575],[577,3210,3211],{"xmlns":579},[581,3212,3213,3232],{},[584,3214,3215,3221,3223,3225,3227,3229],{},[702,3216,3217,3219],{},[587,3218,589],{},[587,3220,604],{},[591,3222,1521],{},[707,3224,2814],{},[587,3226,604],{},[591,3228,1521],{},[707,3230,3231],{},"4",[609,3233,3234],{"encoding":611},"f_y = 2y = 4",[568,3236,3238,3293,3315],{"className":3237,"ariaHidden":600},[616],[568,3239,3241,3244,3284,3287,3290],{"className":3240},[620],[568,3242],{"className":3243,"style":1446},[624],[568,3245,3247,3250],{"className":3246},[629],[568,3248,589],{"className":3249,"style":631},[629,630],[568,3251,3253],{"className":3252},[744],[568,3254,3256,3276],{"className":3255},[748,749],[568,3257,3259,3273],{"className":3258},[753],[568,3260,3262],{"className":3261,"style":1362},[757],[568,3263,3264,3267],{"style":1365},[568,3265],{"className":3266,"style":766},[765],[568,3268,3270],{"className":3269},[770,771,772,773],[568,3271,604],{"className":3272,"style":651},[629,630,773],[568,3274,781],{"className":3275},[780],[568,3277,3279],{"className":3278},[753],[568,3280,3282],{"className":3281,"style":1485},[757],[568,3283],{},[568,3285],{"className":3286,"style":1682},[646],[568,3288,1521],{"className":3289},[1686],[568,3291],{"className":3292,"style":1682},[646],[568,3294,3296,3300,3303,3306,3309,3312],{"className":3295},[620],[568,3297],{"className":3298,"style":3299},[624],"height:0.8389em;vertical-align:-0.1944em;",[568,3301,2814],{"className":3302},[629],[568,3304,604],{"className":3305,"style":651},[629,630],[568,3307],{"className":3308,"style":1682},[646],[568,3310,1521],{"className":3311},[1686],[568,3313],{"className":3314,"style":1682},[646],[568,3316,3318,3321],{"className":3317},[620],[568,3319],{"className":3320,"style":2571},[624],[568,3322,3231],{"className":3323},[629],":",[568,3326,3328],{"className":3327},[1496],[568,3329,3331,3393],{"className":3330},[571],[568,3332,3334],{"className":3333},[575],[577,3335,3336],{"xmlns":579,"display":1505},[581,3337,3338,3390],{},[584,3339,3340,3342,3344,3346,3348,3350,3352,3354,3356,3358,3360,3362,3364,3366,3368,3370,3372,3374,3376,3378,3380,3382,3384,3386,3388],{},[587,3341,2143],{},[591,3343,1521],{},[707,3345,3030],{},[591,3347,2817],{},[707,3349,2814],{},[591,3351,594],{"stretchy":593},[587,3353,597],{},[591,3355,1609],{},[707,3357,1612],{},[591,3359,607],{"stretchy":593},[591,3361,2817],{},[707,3363,3231],{},[591,3365,594],{"stretchy":593},[587,3367,604],{},[591,3369,1609],{},[707,3371,2814],{},[591,3373,607],{"stretchy":593},[591,3375,1521],{},[707,3377,2814],{},[587,3379,597],{},[591,3381,2817],{},[707,3383,3231],{},[587,3385,604],{},[591,3387,1609],{},[707,3389,3030],{},[609,3391,3392],{"encoding":611},"z = 5 + 2(x - 1) + 4(y - 2) = 2x + 4y - 5",[568,3394,3396,3414,3433,3457,3478,3502,3523,3544,3565],{"className":3395,"ariaHidden":600},[616],[568,3397,3399,3402,3405,3408,3411],{"className":3398},[620],[568,3400],{"className":3401,"style":1309},[624],[568,3403,2143],{"className":3404,"style":2191},[629,630],[568,3406],{"className":3407,"style":1682},[646],[568,3409,1521],{"className":3410},[1686],[568,3412],{"className":3413,"style":1682},[646],[568,3415,3417,3421,3424,3427,3430],{"className":3416},[620],[568,3418],{"className":3419,"style":3420},[624],"height:0.7278em;vertical-align:-0.0833em;",[568,3422,3030],{"className":3423},[629],[568,3425],{"className":3426,"style":2439},[646],[568,3428,2817],{"className":3429},[2443],[568,3431],{"className":3432,"style":2439},[646],[568,3434,3436,3439,3442,3445,3448,3451,3454],{"className":3435},[620],[568,3437],{"className":3438,"style":625},[624],[568,3440,2814],{"className":3441},[629],[568,3443,594],{"className":3444},[635],[568,3446,597],{"className":3447},[629,630],[568,3449],{"className":3450,"style":2439},[646],[568,3452,1609],{"className":3453},[2443],[568,3455],{"className":3456,"style":2439},[646],[568,3458,3460,3463,3466,3469,3472,3475],{"className":3459},[620],[568,3461],{"className":3462,"style":625},[624],[568,3464,1612],{"className":3465},[629],[568,3467,607],{"className":3468},[655],[568,3470],{"className":3471,"style":2439},[646],[568,3473,2817],{"className":3474},[2443],[568,3476],{"className":3477,"style":2439},[646],[568,3479,3481,3484,3487,3490,3493,3496,3499],{"className":3480},[620],[568,3482],{"className":3483,"style":625},[624],[568,3485,3231],{"className":3486},[629],[568,3488,594],{"className":3489},[635],[568,3491,604],{"className":3492,"style":651},[629,630],[568,3494],{"className":3495,"style":2439},[646],[568,3497,1609],{"className":3498},[2443],[568,3500],{"className":3501,"style":2439},[646],[568,3503,3505,3508,3511,3514,3517,3520],{"className":3504},[620],[568,3506],{"className":3507,"style":625},[624],[568,3509,2814],{"className":3510},[629],[568,3512,607],{"className":3513},[655],[568,3515],{"className":3516,"style":1682},[646],[568,3518,1521],{"className":3519},[1686],[568,3521],{"className":3522,"style":1682},[646],[568,3524,3526,3529,3532,3535,3538,3541],{"className":3525},[620],[568,3527],{"className":3528,"style":3420},[624],[568,3530,2814],{"className":3531},[629],[568,3533,597],{"className":3534},[629,630],[568,3536],{"className":3537,"style":2439},[646],[568,3539,2817],{"className":3540},[2443],[568,3542],{"className":3543,"style":2439},[646],[568,3545,3547,3550,3553,3556,3559,3562],{"className":3546},[620],[568,3548],{"className":3549,"style":3299},[624],[568,3551,3231],{"className":3552},[629],[568,3554,604],{"className":3555,"style":651},[629,630],[568,3557],{"className":3558,"style":2439},[646],[568,3560,1609],{"className":3561},[2443],[568,3563],{"className":3564,"style":2439},[646],[568,3566,3568,3571],{"className":3567},[620],[568,3569],{"className":3570,"style":2571},[624],[568,3572,3030],{"className":3573},[629],[564,3575,3576,3577,3658,3659,3787,3788,3950,3951,1012],{},"Als Näherung an der Stelle ",[568,3578,3580,3609],{"className":3579},[571],[568,3581,3583],{"className":3582},[575],[577,3584,3585],{"xmlns":579},[581,3586,3587,3606],{},[584,3588,3589,3591,3594,3597,3601,3604],{},[591,3590,594],{"stretchy":593},[707,3592,3593],{},"1,1",[591,3595,3596],{"separator":600},";",[3598,3599,3600],"mtext",{}," ",[707,3602,3603],{},"1,9",[591,3605,607],{"stretchy":593},[609,3607,3608],{"encoding":611},"(1{,}1;\\ 1{,}9)",[568,3610,3612],{"className":3611,"ariaHidden":600},[616],[568,3613,3615,3618,3621,3624,3630,3633,3636,3639,3642,3645,3651,3655],{"className":3614},[620],[568,3616],{"className":3617,"style":625},[624],[568,3619,594],{"className":3620},[635],[568,3622,1612],{"className":3623},[629],[568,3625,3627],{"className":3626},[629],[568,3628,601],{"className":3629},[642],[568,3631,1612],{"className":3632},[629],[568,3634,3596],{"className":3635},[642],[568,3637,3600],{"className":3638},[646],[568,3640],{"className":3641,"style":647},[646],[568,3643,1612],{"className":3644},[629],[568,3646,3648],{"className":3647},[629],[568,3649,601],{"className":3650},[642],[568,3652,3654],{"className":3653},[629],"9",[568,3656,607],{"className":3657},[655]," liefert die Ebene ",[568,3660,3662,3691],{"className":3661},[571],[568,3663,3665],{"className":3664},[575],[577,3666,3667],{"xmlns":579},[581,3668,3669,3688],{},[584,3670,3671,3674,3676,3679,3681,3683,3685],{},[707,3672,3673],{},"2,2",[591,3675,2817],{},[707,3677,3678],{},"7,6",[591,3680,1609],{},[707,3682,3030],{},[591,3684,1521],{},[707,3686,3687],{},"4,8",[609,3689,3690],{"encoding":611},"2{,}2 + 7{,}6 - 5 = 4{,}8",[568,3692,3694,3721,3750,3768],{"className":3693,"ariaHidden":600},[616],[568,3695,3697,3700,3703,3709,3712,3715,3718],{"className":3696},[620],[568,3698],{"className":3699,"style":3299},[624],[568,3701,2814],{"className":3702},[629],[568,3704,3706],{"className":3705},[629],[568,3707,601],{"className":3708},[642],[568,3710,2814],{"className":3711},[629],[568,3713],{"className":3714,"style":2439},[646],[568,3716,2817],{"className":3717},[2443],[568,3719],{"className":3720,"style":2439},[646],[568,3722,3724,3727,3731,3737,3741,3744,3747],{"className":3723},[620],[568,3725],{"className":3726,"style":3299},[624],[568,3728,3730],{"className":3729},[629],"7",[568,3732,3734],{"className":3733},[629],[568,3735,601],{"className":3736},[642],[568,3738,3740],{"className":3739},[629],"6",[568,3742],{"className":3743,"style":2439},[646],[568,3745,1609],{"className":3746},[2443],[568,3748],{"className":3749,"style":2439},[646],[568,3751,3753,3756,3759,3762,3765],{"className":3752},[620],[568,3754],{"className":3755,"style":2571},[624],[568,3757,3030],{"className":3758},[629],[568,3760],{"className":3761,"style":1682},[646],[568,3763,1521],{"className":3764},[1686],[568,3766],{"className":3767,"style":1682},[646],[568,3769,3771,3774,3777,3783],{"className":3770},[620],[568,3772],{"className":3773,"style":3299},[624],[568,3775,3231],{"className":3776},[629],[568,3778,3780],{"className":3779},[629],[568,3781,601],{"className":3782},[642],[568,3784,3786],{"className":3785},[629],"8",", der exakte Wert ist ",[568,3789,3791,3822],{"className":3790},[571],[568,3792,3794],{"className":3793},[575],[577,3795,3796],{"xmlns":579},[581,3797,3798,3819],{},[584,3799,3800,3806,3808,3814,3816],{},[2808,3801,3802,3804],{},[707,3803,3593],{},[707,3805,2814],{},[591,3807,2817],{},[2808,3809,3810,3812],{},[707,3811,3603],{},[707,3813,2814],{},[591,3815,1521],{},[707,3817,3818],{},"4,82",[609,3820,3821],{"encoding":611},"1{,}1^2 + 1{,}9^2 = 4{,}82",[568,3823,3825,3878,3931],{"className":3824,"ariaHidden":600},[616],[568,3826,3828,3831,3834,3840,3869,3872,3875],{"className":3827},[620],[568,3829],{"className":3830,"style":2919},[624],[568,3832,1612],{"className":3833},[629],[568,3835,3837],{"className":3836},[629],[568,3838,601],{"className":3839},[642],[568,3841,3843,3846],{"className":3842},[629],[568,3844,1612],{"className":3845},[629],[568,3847,3849],{"className":3848},[744],[568,3850,3852],{"className":3851},[748],[568,3853,3855],{"className":3854},[753],[568,3856,3858],{"className":3857,"style":2891},[757],[568,3859,3860,3863],{"style":2894},[568,3861],{"className":3862,"style":766},[765],[568,3864,3866],{"className":3865},[770,771,772,773],[568,3867,2814],{"className":3868},[629,773],[568,3870],{"className":3871,"style":2439},[646],[568,3873,2817],{"className":3874},[2443],[568,3876],{"className":3877,"style":2439},[646],[568,3879,3881,3884,3887,3893,3922,3925,3928],{"className":3880},[620],[568,3882],{"className":3883,"style":2919},[624],[568,3885,1612],{"className":3886},[629],[568,3888,3890],{"className":3889},[629],[568,3891,601],{"className":3892},[642],[568,3894,3896,3899],{"className":3895},[629],[568,3897,3654],{"className":3898},[629],[568,3900,3902],{"className":3901},[744],[568,3903,3905],{"className":3904},[748],[568,3906,3908],{"className":3907},[753],[568,3909,3911],{"className":3910,"style":2891},[757],[568,3912,3913,3916],{"style":2894},[568,3914],{"className":3915,"style":766},[765],[568,3917,3919],{"className":3918},[770,771,772,773],[568,3920,2814],{"className":3921},[629,773],[568,3923],{"className":3924,"style":1682},[646],[568,3926,1521],{"className":3927},[1686],[568,3929],{"className":3930,"style":1682},[646],[568,3932,3934,3937,3940,3946],{"className":3933},[620],[568,3935],{"className":3936,"style":3299},[624],[568,3938,3231],{"className":3939},[629],[568,3941,3943],{"className":3942},[629],[568,3944,601],{"className":3945},[642],[568,3947,3949],{"className":3948},[629],"82",". Ein Normalenvektor ist ",[568,3952,3954,3987],{"className":3953},[571],[568,3955,3957],{"className":3956},[575],[577,3958,3959],{"xmlns":579},[581,3960,3961,3984],{},[584,3962,3963,3965,3967,3969,3971,3973,3975,3977],{},[591,3964,594],{"stretchy":593},[707,3966,2814],{},[591,3968,601],{"separator":600},[707,3970,3231],{},[591,3972,601],{"separator":600},[591,3974,1609],{},[707,3976,1612],{},[2808,3978,3979,3981],{},[591,3980,607],{"stretchy":593},[587,3982,3983],{},"T",[609,3985,3986],{"encoding":611},"(2, 4, -1)^T",[568,3988,3990],{"className":3989,"ariaHidden":600},[616],[568,3991,3993,3997,4000,4003,4006,4009,4012,4015,4018,4021,4024],{"className":3992},[620],[568,3994],{"className":3995,"style":3996},[624],"height:1.0913em;vertical-align:-0.25em;",[568,3998,594],{"className":3999},[635],[568,4001,2814],{"className":4002},[629],[568,4004,601],{"className":4005},[642],[568,4007],{"className":4008,"style":647},[646],[568,4010,3231],{"className":4011},[629],[568,4013,601],{"className":4014},[642],[568,4016],{"className":4017,"style":647},[646],[568,4019,1609],{"className":4020},[629],[568,4022,1612],{"className":4023},[629],[568,4025,4027,4030],{"className":4026},[655],[568,4028,607],{"className":4029},[655],[568,4031,4033],{"className":4032},[744],[568,4034,4036],{"className":4035},[748],[568,4037,4039],{"className":4038},[753],[568,4040,4043],{"className":4041,"style":4042},[757],"height:0.8413em;",[568,4044,4045,4048],{"style":2894},[568,4046],{"className":4047,"style":766},[765],[568,4049,4051],{"className":4050},[770,771,772,773],[568,4052,3983],{"className":4053,"style":2166},[629,630,773],[564,4055,4056,4057,4242,4243,4308,4309,4535,4536,1012],{},"Die Kugel ",[568,4058,4060,4098],{"className":4059},[571],[568,4061,4063],{"className":4062},[575],[577,4064,4065],{"xmlns":579},[581,4066,4067,4095],{},[584,4068,4069,4075,4077,4083,4085,4091,4093],{},[2808,4070,4071,4073],{},[587,4072,597],{},[707,4074,2814],{},[591,4076,2817],{},[2808,4078,4079,4081],{},[587,4080,604],{},[707,4082,2814],{},[591,4084,2817],{},[2808,4086,4087,4089],{},[587,4088,2143],{},[707,4090,2814],{},[591,4092,1521],{},[707,4094,3654],{},[609,4096,4097],{"encoding":611},"x^2 + y^2 + z^2 = 9",[568,4099,4101,4145,4189,4233],{"className":4100,"ariaHidden":600},[616],[568,4102,4104,4107,4136,4139,4142],{"className":4103},[620],[568,4105],{"className":4106,"style":2872},[624],[568,4108,4110,4113],{"className":4109},[629],[568,4111,597],{"className":4112},[629,630],[568,4114,4116],{"className":4115},[744],[568,4117,4119],{"className":4118},[748],[568,4120,4122],{"className":4121},[753],[568,4123,4125],{"className":4124,"style":2891},[757],[568,4126,4127,4130],{"style":2894},[568,4128],{"className":4129,"style":766},[765],[568,4131,4133],{"className":4132},[770,771,772,773],[568,4134,2814],{"className":4135},[629,773],[568,4137],{"className":4138,"style":2439},[646],[568,4140,2817],{"className":4141},[2443],[568,4143],{"className":4144,"style":2439},[646],[568,4146,4148,4151,4180,4183,4186],{"className":4147},[620],[568,4149],{"className":4150,"style":2919},[624],[568,4152,4154,4157],{"className":4153},[629],[568,4155,604],{"className":4156,"style":651},[629,630],[568,4158,4160],{"className":4159},[744],[568,4161,4163],{"className":4162},[748],[568,4164,4166],{"className":4165},[753],[568,4167,4169],{"className":4168,"style":2891},[757],[568,4170,4171,4174],{"style":2894},[568,4172],{"className":4173,"style":766},[765],[568,4175,4177],{"className":4176},[770,771,772,773],[568,4178,2814],{"className":4179},[629,773],[568,4181],{"className":4182,"style":2439},[646],[568,4184,2817],{"className":4185},[2443],[568,4187],{"className":4188,"style":2439},[646],[568,4190,4192,4195,4224,4227,4230],{"className":4191},[620],[568,4193],{"className":4194,"style":2891},[624],[568,4196,4198,4201],{"className":4197},[629],[568,4199,2143],{"className":4200,"style":2191},[629,630],[568,4202,4204],{"className":4203},[744],[568,4205,4207],{"className":4206},[748],[568,4208,4210],{"className":4209},[753],[568,4211,4213],{"className":4212,"style":2891},[757],[568,4214,4215,4218],{"style":2894},[568,4216],{"className":4217,"style":766},[765],[568,4219,4221],{"className":4220},[770,771,772,773],[568,4222,2814],{"className":4223},[629,773],[568,4225],{"className":4226,"style":1682},[646],[568,4228,1521],{"className":4229},[1686],[568,4231],{"className":4232,"style":1682},[646],[568,4234,4236,4239],{"className":4235},[620],[568,4237],{"className":4238,"style":2571},[624],[568,4240,3654],{"className":4241},[629]," enthält den Punkt ",[568,4244,4246,4272],{"className":4245},[571],[568,4247,4249],{"className":4248},[575],[577,4250,4251],{"xmlns":579},[581,4252,4253,4269],{},[584,4254,4255,4257,4259,4261,4263,4265,4267],{},[591,4256,594],{"stretchy":593},[707,4258,1612],{},[591,4260,601],{"separator":600},[707,4262,2814],{},[591,4264,601],{"separator":600},[707,4266,2814],{},[591,4268,607],{"stretchy":593},[609,4270,4271],{"encoding":611},"(1, 2, 2)",[568,4273,4275],{"className":4274,"ariaHidden":600},[616],[568,4276,4278,4281,4284,4287,4290,4293,4296,4299,4302,4305],{"className":4277},[620],[568,4279],{"className":4280,"style":625},[624],[568,4282,594],{"className":4283},[635],[568,4285,1612],{"className":4286},[629],[568,4288,601],{"className":4289},[642],[568,4291],{"className":4292,"style":647},[646],[568,4294,2814],{"className":4295},[629],[568,4297,601],{"className":4298},[642],[568,4300],{"className":4301,"style":647},[646],[568,4303,2814],{"className":4304},[629],[568,4306,607],{"className":4307},[655],". Mit ",[568,4310,4312,4374],{"className":4311},[571],[568,4313,4315],{"className":4314},[575],[577,4316,4317],{"xmlns":579},[581,4318,4319,4371],{},[584,4320,4321,4323,4325,4327,4329,4331,4333,4335,4337,4339,4341,4343,4345,4351,4353,4355,4357,4359,4361,4363,4365],{},[587,4322,2229],{"mathvariant":2228},[587,4324,2130],{},[591,4326,1521],{},[591,4328,594],{"stretchy":593},[707,4330,2814],{},[587,4332,597],{},[591,4334,601],{"separator":600},[707,4336,2814],{},[587,4338,604],{},[591,4340,601],{"separator":600},[707,4342,2814],{},[587,4344,2143],{},[2808,4346,4347,4349],{},[591,4348,607],{"stretchy":593},[587,4350,3983],{},[591,4352,1521],{},[591,4354,594],{"stretchy":593},[707,4356,2814],{},[591,4358,601],{"separator":600},[707,4360,3231],{},[591,4362,601],{"separator":600},[707,4364,3231],{},[2808,4366,4367,4369],{},[591,4368,607],{"stretchy":593},[587,4370,3983],{},[609,4372,4373],{"encoding":611},"\\nabla F = (2x, 2y, 2z)^T = (2, 4, 4)^T",[568,4375,4377,4399,4476],{"className":4376,"ariaHidden":600},[616],[568,4378,4380,4384,4387,4390,4393,4396],{"className":4379},[620],[568,4381],{"className":4382,"style":4383},[624],"height:0.6833em;",[568,4385,2229],{"className":4386},[629],[568,4388,2130],{"className":4389,"style":2166},[629,630],[568,4391],{"className":4392,"style":1682},[646],[568,4394,1521],{"className":4395},[1686],[568,4397],{"className":4398,"style":1682},[646],[568,4400,4402,4405,4408,4411,4414,4417,4420,4423,4426,4429,4432,4435,4438,4467,4470,4473],{"className":4401},[620],[568,4403],{"className":4404,"style":3996},[624],[568,4406,594],{"className":4407},[635],[568,4409,2814],{"className":4410},[629],[568,4412,597],{"className":4413},[629,630],[568,4415,601],{"className":4416},[642],[568,4418],{"className":4419,"style":647},[646],[568,4421,2814],{"className":4422},[629],[568,4424,604],{"className":4425,"style":651},[629,630],[568,4427,601],{"className":4428},[642],[568,4430],{"className":4431,"style":647},[646],[568,4433,2814],{"className":4434},[629],[568,4436,2143],{"className":4437,"style":2191},[629,630],[568,4439,4441,4444],{"className":4440},[655],[568,4442,607],{"className":4443},[655],[568,4445,4447],{"className":4446},[744],[568,4448,4450],{"className":4449},[748],[568,4451,4453],{"className":4452},[753],[568,4454,4456],{"className":4455,"style":4042},[757],[568,4457,4458,4461],{"style":2894},[568,4459],{"className":4460,"style":766},[765],[568,4462,4464],{"className":4463},[770,771,772,773],[568,4465,3983],{"className":4466,"style":2166},[629,630,773],[568,4468],{"className":4469,"style":1682},[646],[568,4471,1521],{"className":4472},[1686],[568,4474],{"className":4475,"style":1682},[646],[568,4477,4479,4482,4485,4488,4491,4494,4497,4500,4503,4506],{"className":4478},[620],[568,4480],{"className":4481,"style":3996},[624],[568,4483,594],{"className":4484},[635],[568,4486,2814],{"className":4487},[629],[568,4489,601],{"className":4490},[642],[568,4492],{"className":4493,"style":647},[646],[568,4495,3231],{"className":4496},[629],[568,4498,601],{"className":4499},[642],[568,4501],{"className":4502,"style":647},[646],[568,4504,3231],{"className":4505},[629],[568,4507,4509,4512],{"className":4508},[655],[568,4510,607],{"className":4511},[655],[568,4513,4515],{"className":4514},[744],[568,4516,4518],{"className":4517},[748],[568,4519,4521],{"className":4520},[753],[568,4522,4524],{"className":4523,"style":4042},[757],[568,4525,4526,4529],{"style":2894},[568,4527],{"className":4528,"style":766},[765],[568,4530,4532],{"className":4531},[770,771,772,773],[568,4533,3983],{"className":4534,"style":2166},[629,630,773]," ergibt sich die Tangentialebene ",[568,4537,4539,4572],{"className":4538},[571],[568,4540,4542],{"className":4541},[575],[577,4543,4544],{"xmlns":579},[581,4545,4546,4569],{},[584,4547,4548,4550,4552,4554,4556,4558,4560,4562,4564,4566],{},[707,4549,2814],{},[587,4551,597],{},[591,4553,2817],{},[707,4555,3231],{},[587,4557,604],{},[591,4559,2817],{},[707,4561,3231],{},[587,4563,2143],{},[591,4565,1521],{},[707,4567,4568],{},"18",[609,4570,4571],{"encoding":611},"2x + 4y + 4z = 18",[568,4573,4575,4596,4617,4638],{"className":4574,"ariaHidden":600},[616],[568,4576,4578,4581,4584,4587,4590,4593],{"className":4577},[620],[568,4579],{"className":4580,"style":3420},[624],[568,4582,2814],{"className":4583},[629],[568,4585,597],{"className":4586},[629,630],[568,4588],{"className":4589,"style":2439},[646],[568,4591,2817],{"className":4592},[2443],[568,4594],{"className":4595,"style":2439},[646],[568,4597,4599,4602,4605,4608,4611,4614],{"className":4598},[620],[568,4600],{"className":4601,"style":3299},[624],[568,4603,3231],{"className":4604},[629],[568,4606,604],{"className":4607,"style":651},[629,630],[568,4609],{"className":4610,"style":2439},[646],[568,4612,2817],{"className":4613},[2443],[568,4615],{"className":4616,"style":2439},[646],[568,4618,4620,4623,4626,4629,4632,4635],{"className":4619},[620],[568,4621],{"className":4622,"style":2571},[624],[568,4624,3231],{"className":4625},[629],[568,4627,2143],{"className":4628,"style":2191},[629,630],[568,4630],{"className":4631,"style":1682},[646],[568,4633,1521],{"className":4634},[1686],[568,4636],{"className":4637,"style":1682},[646],[568,4639,4641,4644],{"className":4640},[620],[568,4642],{"className":4643,"style":2571},[624],[568,4645,4568],{"className":4646},[629],[559,4648,4650],{"id":4649},"typische-fehler","Typische Fehler",[4652,4653,4654,4715,4858,5032],"ul",{},[4655,4656,4657,4658,3202,4686,4714],"li",{},"Die partiellen Ableitungen allgemein stehen lassen, statt sie im Berührpunkt auszuwerten. Die Gleichung einer Ebene darf nur linear in ",[568,4659,4661,4674],{"className":4660},[571],[568,4662,4664],{"className":4663},[575],[577,4665,4666],{"xmlns":579},[581,4667,4668,4672],{},[584,4669,4670],{},[587,4671,597],{},[609,4673,597],{"encoding":611},[568,4675,4677],{"className":4676,"ariaHidden":600},[616],[568,4678,4680,4683],{"className":4679},[620],[568,4681],{"className":4682,"style":1309},[624],[568,4684,597],{"className":4685},[629,630],[568,4687,4689,4702],{"className":4688},[571],[568,4690,4692],{"className":4691},[575],[577,4693,4694],{"xmlns":579},[581,4695,4696,4700],{},[584,4697,4698],{},[587,4699,604],{},[609,4701,604],{"encoding":611},[568,4703,4705],{"className":4704,"ariaHidden":600},[616],[568,4706,4708,4711],{"className":4707},[620],[568,4709],{"className":4710,"style":1412},[624],[568,4712,604],{"className":4713,"style":651},[629,630]," sein.",[4655,4716,4717,4718,4857],{},"Den Funktionswert ",[568,4719,4721,4753],{"className":4720},[571],[568,4722,4724],{"className":4723},[575],[577,4725,4726],{"xmlns":579},[581,4727,4728,4750],{},[584,4729,4730,4732,4734,4740,4742,4748],{},[587,4731,589],{},[591,4733,594],{"stretchy":593},[702,4735,4736,4738],{},[587,4737,597],{},[707,4739,709],{},[591,4741,601],{"separator":600},[702,4743,4744,4746],{},[587,4745,604],{},[707,4747,709],{},[591,4749,607],{"stretchy":593},[609,4751,4752],{"encoding":611},"f(x_0, y_0)",[568,4754,4756],{"className":4755,"ariaHidden":600},[616],[568,4757,4759,4762,4765,4768,4808,4811,4814,4854],{"className":4758},[620],[568,4760],{"className":4761,"style":625},[624],[568,4763,589],{"className":4764,"style":631},[629,630],[568,4766,594],{"className":4767},[635],[568,4769,4771,4774],{"className":4770},[629],[568,4772,597],{"className":4773},[629,630],[568,4775,4777],{"className":4776},[744],[568,4778,4780,4800],{"className":4779},[748,749],[568,4781,4783,4797],{"className":4782},[753],[568,4784,4786],{"className":4785,"style":758},[757],[568,4787,4788,4791],{"style":761},[568,4789],{"className":4790,"style":766},[765],[568,4792,4794],{"className":4793},[770,771,772,773],[568,4795,709],{"className":4796},[629,773],[568,4798,781],{"className":4799},[780],[568,4801,4803],{"className":4802},[753],[568,4804,4806],{"className":4805,"style":788},[757],[568,4807],{},[568,4809,601],{"className":4810},[642],[568,4812],{"className":4813,"style":647},[646],[568,4815,4817,4820],{"className":4816},[629],[568,4818,604],{"className":4819,"style":651},[629,630],[568,4821,4823],{"className":4822},[744],[568,4824,4826,4846],{"className":4825},[748,749],[568,4827,4829,4843],{"className":4828},[753],[568,4830,4832],{"className":4831,"style":758},[757],[568,4833,4834,4837],{"style":817},[568,4835],{"className":4836,"style":766},[765],[568,4838,4840],{"className":4839},[770,771,772,773],[568,4841,709],{"className":4842},[629,773],[568,4844,781],{"className":4845},[780],[568,4847,4849],{"className":4848},[753],[568,4850,4852],{"className":4851,"style":788},[757],[568,4853],{},[568,4855,607],{"className":4856},[655]," vergessen. Dann geht die Ebene nicht durch den Berührpunkt.",[4655,4859,4860,4861,4895,4896,5031],{},"Beim Normalenvektor die dritte Komponente ",[568,4862,4864,4880],{"className":4863},[571],[568,4865,4867],{"className":4866},[575],[577,4868,4869],{"xmlns":579},[581,4870,4871,4877],{},[584,4872,4873,4875],{},[591,4874,1609],{},[707,4876,1612],{},[609,4878,4879],{"encoding":611},"-1",[568,4881,4883],{"className":4882,"ariaHidden":600},[616],[568,4884,4886,4889,4892],{"className":4885},[620],[568,4887],{"className":4888,"style":3420},[624],[568,4890,1609],{"className":4891},[629],[568,4893,1612],{"className":4894},[629]," weglassen oder ",[568,4897,4899,4929],{"className":4898},[571],[568,4900,4902],{"className":4901},[575],[577,4903,4904],{"xmlns":579},[581,4905,4906,4926],{},[584,4907,4908,4910,4916,4918,4924],{},[591,4909,594],{"stretchy":593},[702,4911,4912,4914],{},[587,4913,589],{},[587,4915,597],{},[591,4917,601],{"separator":600},[702,4919,4920,4922],{},[587,4921,589],{},[587,4923,604],{},[591,4925,607],{"stretchy":593},[609,4927,4928],{"encoding":611},"(f_x, f_y)",[568,4930,4932],{"className":4931,"ariaHidden":600},[616],[568,4933,4935,4939,4942,4982,4985,4988,5028],{"className":4934},[620],[568,4936],{"className":4937,"style":4938},[624],"height:1.0361em;vertical-align:-0.2861em;",[568,4940,594],{"className":4941},[635],[568,4943,4945,4948],{"className":4944},[629],[568,4946,589],{"className":4947,"style":631},[629,630],[568,4949,4951],{"className":4950},[744],[568,4952,4954,4974],{"className":4953},[748,749],[568,4955,4957,4971],{"className":4956},[753],[568,4958,4960],{"className":4959,"style":1362},[757],[568,4961,4962,4965],{"style":1365},[568,4963],{"className":4964,"style":766},[765],[568,4966,4968],{"className":4967},[770,771,772,773],[568,4969,597],{"className":4970},[629,630,773],[568,4972,781],{"className":4973},[780],[568,4975,4977],{"className":4976},[753],[568,4978,4980],{"className":4979,"style":788},[757],[568,4981],{},[568,4983,601],{"className":4984},[642],[568,4986],{"className":4987,"style":647},[646],[568,4989,4991,4994],{"className":4990},[629],[568,4992,589],{"className":4993,"style":631},[629,630],[568,4995,4997],{"className":4996},[744],[568,4998,5000,5020],{"className":4999},[748,749],[568,5001,5003,5017],{"className":5002},[753],[568,5004,5006],{"className":5005,"style":1362},[757],[568,5007,5008,5011],{"style":1365},[568,5009],{"className":5010,"style":766},[765],[568,5012,5014],{"className":5013},[770,771,772,773],[568,5015,604],{"className":5016,"style":651},[629,630,773],[568,5018,781],{"className":5019},[780],[568,5021,5023],{"className":5022},[753],[568,5024,5026],{"className":5025,"style":1485},[757],[568,5027],{},[568,5029,607],{"className":5030},[655]," als Normalenvektor im Raum ansehen.",[4655,5033,5034,5035,5063],{},"Eine Tangentialebene angeben, obwohl ",[568,5036,5038,5051],{"className":5037},[571],[568,5039,5041],{"className":5040},[575],[577,5042,5043],{"xmlns":579},[581,5044,5045,5049],{},[584,5046,5047],{},[587,5048,589],{},[609,5050,589],{"encoding":611},[568,5052,5054],{"className":5053,"ariaHidden":600},[616],[568,5055,5057,5060],{"className":5056},[620],[568,5058],{"className":5059,"style":682},[624],[568,5061,589],{"className":5062,"style":631},[629,630]," nur partiell differenzierbar ist. Ohne totale Differenzierbarkeit schmiegt sich die Ebene nicht unbedingt an.",{"title":5065,"searchDepth":5066,"depth":5066,"links":5067},"",2,[5068,5069,5070],{"id":561,"depth":5066,"text":562},{"id":2776,"depth":5066,"text":2777},{"id":4649,"depth":5066,"text":4650},[5072,5074,5077,5080,5083,5085,5087,5089],{"lhs":5073,"rhs":3030},"1^2 + 2^2",{"lhs":5075,"rhs":5076},"5 + 2*(x - 1) + 4*(y - 2)","2*x + 4*y - 5",{"lhs":5078,"rhs":5079},"2*1.1 + 4*1.9 - 5","4.8",{"lhs":5081,"rhs":5082},"1.1^2 + 1.9^2","4.82",{"lhs":5084,"rhs":709},"dot([2, 4, -1], [1, 0, 2])",{"lhs":5086,"rhs":709},"dot([2, 4, -1], [0, 1, 4])",{"lhs":5088,"rhs":3654},"1^2 + 2^2 + 2^2",{"lhs":5090,"rhs":4568},"2*1 + 4*2 + 4*2","f \\text{ in } (x_0, y_0) \\text{ (total) differenzierbar}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">in\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(x_0, y_0)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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