Can you help me with all the parts of this question (a, b, c, d)?

-y2 Define the function f(x, y) = x2 ty 2 (a, y) + (0, 0) 0 (x, y) = (0, 0) (a) Verify that for (x, y) * (0, 0), Ox f(x, y) _ y(* +4x 2 -y4) dy f(x, y) = (x-4xy -4) ( ac 2 + 2) 2 and ( ac 2 + y 2 ) 2 (b) Use the limit definition of the partial derivative to show that Ox f(0, 0) = 0 and Of(0, 0) = 0. Continuing to use the limit definition, show that OyOx f(0, 0) and Ox dyf(0, 0) both exist but aren't equal. (c) When (x, y) * (0, 0), show that Or dy f(x, y) = dyOx f(x, y) = x6+9xy2-9xy*-y Using this result, show that ( 20 2 + y 2 ) 3 limn 0 Ox dy f(h, 0) # limn +0 Oxy f(0, h) so that this mixed partial derivative is not continuous at (0,0). (d) Why doesn't part (b) contradict Clairaut's theorem