# 微積分考古題(王子請幫幫忙)

<1>Let f:[a,b][a,b] be a continuously differentiable function. suppose that

max 1f'(x)1<1

a<x<b

prove that there exists a unique solution f(x)-x=0

(Hint:Intermediate Value Theorem and Mean Value Theorem)

<2>find the Maclaurin series of √(1+x) and the radius of convergence

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