Re: [考古] 政大國貿
※ 引述《beingsad (> < )》之銘言：
: 1.Find the interval of convergence of the power series
: ∞ (x-2)^n
: Σ (-1)^n ----------
: n=0 n+1
: √1+√2+√3+....+√n
: 2.lim ----------------------
: n→∞ n^3/2
: x^2
: 3.If ∫ f(t)dt=xcosπx,find f(4)
: 0
: 4.Let f and g be differentiable functions and assume that f(g(x)) = x and
: f'(x)=1+{f(x)}^3. Find g'(x).
: 幫解一下 謝謝~
4. f(g(x)) = x
等號兩邊對 x 微分得
(f'(g(x)))(g'(x)) = 1
1 1
g'(x) = -------- = ---------------
f'(g(x)) 1 + [f(g(x))]^3
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