作者rod24574575 (天然呆)
看板NTU-Exam
標題[試題] 99下 薛克民 微積分甲下 第二次小考
時間Sun Apr 3 16:51:38 2011
課程名稱︰微積分甲下
課程性質︰必修
課程教師︰薛克民
開課學院：電資學院、工學院、管理學院
開課系所︰電機系、資工系、材料系、資管系
考試日期（年月日）︰100/3/7
考試時限（分鐘）：40分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Write down all the details or you may
not get the full grades.
There could be some problems on the
back of the paper.
x sin(t)
A. (a) Find Taylor series for f(x) = ∫ ──── dt and determine the
0 t
interval of convergence. (5%)
x ∞ (-1)^(n-1)
(b) Show that ∫ x^(x) dx = Σ ────── . Hint: Integrate a series
0 n=1 n^(n)
term by term. (5%)
B. Find the sum of
∞ n ∞ n^(2)
(a) Σ ────(5%) (b) Σ ────(5%)
n=1 2^(n) n=1 2^(n)
∞
Hint: Starting with the geometric series Σ x^(n)
n=0
C. (a) Find the Taylor series for ㏑(1+x) (5%)
(1+x)
(b) Find the Taylor series for e (5%)
(1+x) x
Hint: e = e．e
1 x 1
(c) Find the Taylor series for (1 +
──) in porwers of ──to degree
x x
three. (5%)
Hint: Consider it in exponential form and use the rusults of (a), (b).
╭ e 2┌ 1 x ┐ 11 ╮
(d) Evaluate the limit: lim x│
──*x + x │ (1 +
──) - e │- ──*e │
x→∞ ╰ 2 └ x ┘ 24 ╯
(5%)
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※ 編輯: rod24574575 來自: 218.167.197.82 (04/03 16:53)