1. (a) Let u = sin x + y √x + √y' (b) A function f(x, y) defined as 2² u prove that 2 əx² fxy (0,0) fyx (0, 0). f(x, y)

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1. (a) Let u = sin x + y √x + √y' (b) A function f(x, y) defined as 2² u prove that 2 əx² fxy (0,0) fyx (0, 0). f(x, y) = f(x, y) = = + 2xy. 8² u dxdy x²y² x² 0; 5; +y² (x² + y²) tan ㅠ 22 Show that fay and fyr are not continuous at (0, 0) though fry (0,0) = fyx (0,0). (c) Show that for the function -1 + 8² u მყ2 if(x, y) = (0,0) if (x, y) = (0,0) X sin u cos 2u 4 cos³ u : when x 0 when x = 0