課程名稱︰微積分乙下
課程性質︰共同必修
課程教師︰張樹城
開課學院：管院
開課系所︰會計系/財金系/工管系企管組/國企系/地理系/經濟系
考試日期（年月日）︰2011/4/28
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(25%) Compute the followings(5 out of 7)
t
(a)lim(∫(1+x)^100 dx)^(1/t)
t→0 0
∞
(b)∫ e^(-x^2) dx
0
dx
(c)∫------------
9x^2+6x+10
(d)∫x^(-1) lnxdx
(e)∫sin^3x cos^2x dx
(f)∫e^x cosx dx
∞ 1
(g)∫ ------- dx
∞ 1+x^2
2.(10%) Suppose that f(x) is a continuous function difined by
x f(t)
f(x)=2+∫------------ dt, x≧0
0 (t+3)(t+2)
Find (a)f'(x)
(b)f(1)
3.(15%)
(a) Find the area of the region between the curves
x=y^2 and x+y+2
in the first quadrant.
(b) Find the length of the unit circle x^2+y^2=1
(c) Find surface area of the sphere of radius 1 which is generated by
x^2+y^2=1 about the x-axis.
4.沒有第四題
5.(20%) Determine which series converge and which series diverge?
Give reasons for your answers.
∞ 2n
(a)Σ ---------
n=1 n^2-n+1
∞ ln n
(b)Σ (-1)^(n+1) ----
n=1 n
∞ ln n
(c)Σ -----
n=1 n
∞ n^n
(d)Σ -----
n=1 n!
6.(10%)
(a) Find the Maclaurin series for e^x
(b) Estimate e with an error less than 10^(-2)
7.(10%)
Consider the sequence {a } with
n
a =2^(1/2), a =(2+a )^(1/2)
1 n+1 n
(a) Find an upper bound of {a }
n
(b) Find lim a
n→∞ n
8.(10%)
Let Σ be the plane : 3x+2y+6z=6
(a) Find a vector N normal to the plane Σ
(b) Find the distance from the point S(1,1,3) to the plane Σ
9.(10%, Bonus)
(a) Find the Maclaurin series for tan^(-1) x
(b) Show that
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◆ From: 140.112.241.147
※ 編輯: showshiaring 來自: 140.112.241.147 (06/23 16:40)