# Show that the following functions are diﬀerentiable at x = 0.(a) |x| sin x (b) x2/3 sin x (c) 3√x(1−cos x) (d) h(x) ={x2 sin(1/x), x 6 = 00, x = 0.Page 3

## Question

## Solution 1

To show that a function is differentiable at x = 0, we need to check if the function is continuous at x = 0 and if the derivative exists at x = 0.

(a) For the function f(x) = |x| sin x, we can see that it is continuous at x = 0 because both |x| and sin x are continuous functions. To check if the de Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

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