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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
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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solutions for question (i)

Sol4 Чуз ч)з 3sinte) +o°sinly) : ngto flx,y)= X = (1.7) = (0,0) at f waints to be So f fro,0)=0 Continuos at 3en then limit m

Ela B14 Ifcm,y)-os o:8=(8/2) (E12) E>O 314 claim, = tor any Sfcmid)-o)<s 314

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