※ 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
等號兩邊對 x 微分得
(2x)(f(x^2)) = cos(πx) - (πx)(sin(πx))
令 x = 2 代入上式得
(4)(f(4)) = cos(2π) - (2π)(sin(2π)) = 1
1
f(4) = ---
4
: 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~
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