4. Even when a function f(x) is differentiable at x = a, its derivative function f(x) can behave oddly near x = a, in the sense that lim f(x) does not exist. Thus, in general, we cannot compute fº(a) by putting x→a into fº(x), which is calculated by formulas for x 6= a. Let f(x) { x² cos Bo X x→a (a) Show that f(x) is differentiable at x = 0. (b) Write down f(x) explicitly for each x. f'(0) # lim f'(x). (c) Show that x-0 if x #0 if x = 0.

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