# b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš... b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In case they exist, find them. f(x,y) = ||(x, y) || iv. Let f: R2 - R, a = (-1,2), u = (3,-4), v = (12,5) and w = (15,1). If Duf(a) = 8, D,f(a) = 1 find Duf(a). DO 098 BBCO3568 ABCD

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