Iff: 2- is defined by f(x, y) = xy/(x + y) unless x that D.f(0, 0)...

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Iff: 2- is defined by f(x, y) = xy²/(x² + y²) unless x that D.f(0, 0) exists for all v, but f is not differentiable at (0, 0). Hint: Note first that f(tv) = tf(v) for all te and ve ². Then show that D.f(0, 0) = f(v) for all v. Hence y = 0, and f(0, 0) = 0, show Dif(0,0) - D₂f(0, 0) = 0 but D(1, 1)f(0, 0) = 4. Iff: 2- is defined by f(x, y) = xy²/(x² + y²) unless x that D.f(0, 0) exists for all v, but f is not differentiable at (0, 0). Hint: Note first that f(tv) = tf(v) for all te and ve ². Then show that D.f(0, 0) = f(v) for all v. Hence y = 0, and f(0, 0) = 0, show Dif(0,0) - D₂f(0, 0) = 0 but D(1, 1)f(0, 0) = 4.

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To show that Df0 0 exists for all v but f is not differentiable at 0 0 we can follow the given hints ... View the full answer