let-f-x-y-x-2-y-2-sin-1-x-2-y-2-if-x-y-0-0-and-f-0-0-0-prove-that-f-is-differenciable-at-all-point-of-R-2-2-prove-that-f-x-and-f-y-are-not-differdnciable-at-0-0-

Question Number 36176 by prof Abdo imad last updated on 30/May/18

l e t f (x, y) = (x^{2} + y^{2}) s i n {\frac{1}{\sqrt{x^{2} + y^{2}}}} i f (x, y) = (0, 0)

a n d f (0, 0) = 0

p r o v e t h a t f i s d i f f e r e n c i a b l e a t a l l p o i n t o f R^{2}

2) p r o v e t h a t \frac{\partial f}{\partial x} a n d \frac{\partial f}{\partial y} a r e n o t d i f f e r d n c i a b l e

a t (0, 0)