- 15 9 Let F Be A Function Of Two Variables Defined By X Y If X Y 0 0 F X Y X Y 0 If X Y 0 0 1 (216.32 KiB) Viewed 27 times
(15%) 9. Let f be a function of two variables defined by x³ y , if(x, y) = (0,0) f(x, y) = { x² + y² 0 , if(x, y) = (0,0
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(15%) 9. Let f be a function of two variables defined by x³ y , if(x, y) = (0,0) f(x, y) = { x² + y² 0 , if(x, y) = (0,0
(15%) 9. Let f be a function of two variables defined by x³ y , if(x, y) = (0,0) f(x, y) = { x² + y² 0 , if(x, y) = (0,0) Prove the following statements by definition to deduce that f is a counterexample to " differentiability continuity and existence of all directionalderivatives". ● (A) f is continuous at (0,0) ● (B) Daf(0,0) exists for all unit vector u = (a, b), a² + b² = 1 • (C) f is not differentiable at (0,0)
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