課程名稱︰微乙
課程性質︰必修
課程教師︰張秀瑜
開課學院：理學院
開課系所︰經濟／管院／地理
考試日期（年月日）︰2011/4
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是~
（如未明確表示，則不予發放）
試題 :
1.(16%)Evaluate the integral
2 x^2+1
(a)∫________ dx
1 x^2+x
3x+1
(b)∫___________ dx
x^2+2x+5
2.(14%) Evaluate the improper integral
∞
(a)∫ xe^-xλ dx , λis positive
0
∞
(b)∫ (x^2)e^-xλ dx , λis positive
0
3.(16%) (a)Find the radius and the interval of convergence of the series
∞ (x+1)^n
Σ -------
n=0 n2^n
∞ ∞
(b)if ΣCn2^n is convergent, does it follow that ΣCn√3^n is convergent?
n=0 n=0
4.(18%) Determine the series for convergence or divergence
∞ lnx ∞ 1 ∞
(a) Σ ------ (b) Σ ------------- (c) Σ(-1)^n arctan(n)
n=1 e^n n=1 (n^4+1)^1/3 n=1
5.(12%) Find the Tylor polynomial T3(x) of f(x)=sinx at a=π/2 and
use Tylor's formula tp express the reminder term R3(x)
6.(8%) Use the binomial series to find f(6)(0) of f(x)=(x^2+4)^1/2
↑上標
7.(16%) (a) Find the area of the region that lies in the sector
1
r=---- π＜θ＜2π
θ
(b)For the curve in (a), find the slope of the tangent line when
π=θ
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