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50. Suppose that f : R â R and g : R â R are both continuous, and f is differentiable at 0, with f(0) - f(0) 0. Show that h(x) -f (x)g(x) is also differentiable at x 0 and k(0) = 0 . Note that since we do not know that g is differentiable at product rule (even if we knew what that was 0, we cannot use the
50. Suppose that f : R â R and g : R â R are both continuous, and f is differentiable at 0, with f(0) - f(0) 0. Show that h(x) -f (x)g(x) is also differentiable at x 0 and k(0) = 0 . Note that since we do not know that g is differentiable at product rule (even if we knew what that was 0, we cannot use the
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