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Posted: **Wed Jul 13, 2022 5:08 am**

: Problem 14 Let F R2 R Be Defined By Setting F 0 0 And F X Y X2 Y2xy If X Y 0 1 For Which Vectors U 0 Does F 0 1 (75.26 KiB) Viewed 27 times

Problem 14. Let f:R2→R be defined by setting f(0)=0 and f(x,y)=x2+y2xy if (x,y)=0. 1. For which vectors u=0 does f′(0;u) exist? Evaluate it when it exists. 2. Do D1f and D2f exist at 0 ? 3. Is f differentiable at 0 ? 4. Is f continuous at 0 ?

Answer Happy

Problem 14. Let f:R2→R be defined by setting f(0)=0 and f(x,y)=x2+y2xy​ if (x,y)=0. 1. For which vectors u=0 does f′(0

Problem 14. Let f:R2→R be defined by setting f(0)=0 and f(x,y)=x2+y2xy​ if (x,y)=0. 1. For which vectors u=0 does f′(0

Problem 14. Let f:R2→R be defined by setting f(0)=0 and f(x,y)=x2+y2xy if (x,y)=0. 1. For which vectors u=0 does f′(0

Problem 14. Let f:R2→R be defined by setting f(0)=0 and f(x,y)=x2+y2xy if (x,y)=0. 1. For which vectors u=0 does f′(0