The formal definition for the derivative of f(x) at x = a is f'(a) = lim f(a+h) — f(a)/h h→0 (1) Find the Taylor

Question

The formal definition for the derivative of f(x) at x = a is
f'(a) = lim f(a+h) — f(a)/h
         h→0
(1) Find the Taylor polynomial of order 5 about = 2 which approximates f(x) = eˣ.
(ii) Using this approximation, show, from the formal definition of a derivative, that f'(2) = e².

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