Question: Al. Consider the function f : R2 - R given by x272 f(x, y) = x2y2+(x-y)2 if ( x, y) # (0, 0) 0 if

Al. Consider the function f : R2 - R given by

Al. Consider the function f : R2 - R given by x272 f(x, y) = x2y2+(x-y)2 if ( x, y) # (0, 0) 0 if (x, y) = (0,0) Show that the function f satisfies the following: (a) The iterated limits lim lim f(x, y) ) and lim lim f(x, y) ) exist and equal to 0. x-+0 y-+0 y-+0 (b) lim f(x, y) does not exist. (x,y) -(0,0) (c) The function f is not continuous at (0, 0) (d) The partial derivatives exist at (0, 0)

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