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Webgocphim.net Web• Consider the difference between fand its affine approximation at (0,y): r(h,k) = f(h,y+k)− f(0,y)− df(0,y)·(h,k). To prove that f is differentiable at (0,y) with derivative df(0,y), we need to show that lim (h,k)→(0,0) r(h,k) k(h,k)k = 0. • Supposing that [df(0,y)] = (0,0) and using the fact that f(0,y) = 0, we get r(h,k) = f(h ...
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