作者shokanshorin (上官蔷凛)
看板NTU-Exam
标题[试题] 98下 王振男 微积分乙下 期中考
时间Fri Apr 15 17:35:27 2011
课程名称︰微积分乙下
课程性质︰必带
课程教师︰王振男
开课学院：医学院
开课系所︰医学系
考试日期（年月日）︰2010／4／27
考试时限（分钟）：120min
是否需发放奖励金：是
（如未明确表示，则不予发放）
1. For what values of x does the series below converge? What is its sum?
1 1 1
1 - ─(x-1) + ─(x-1)^2 -... + (-─)^n(x-1)^n +...
2 4 2
What series do you get if you differentiate the given series term by term?
For what values of x does the new series converge? What is its sum? (10%)
2. Can you define f(0,0) such that function below is continuous at (0,0)? (10%)
3x^2 - (xy)^2 + 3y^2
f(x,y) = ln (───────────)
x^2 + y^2
3. Find the shortest distance between the parabola y=x^2 and the line x-y=1.
Also, specify the points where the shortest distance occurs. (20%)
(Hint: method of Lagrange multiplier)
4. Find the critical point of f(x,y)= xy + 2x - ln(yx^2) in the open first
quadrant (x＞0,y＞0) and show that f takes on a minimum there. (20%)
5. Show that the improper integral below converges and find its value, where
0＜a＜b. (20%)
∞ e^(-ax) - e^(-bx)
∫ ───────── dx
0 x
e^(-ax) - e^(-bx) b
(Hint: to find its value, observe that ───────── = ∫e^(-xy)dy.)
x a
2 (y+4)/2
6. Evaluate the integral ∫∫ y^3×(2x-y)× e^(2x-y)^2 dxdy (20%)
0 y/2
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1F：推 ouanonym :楼上两位 「自我感觉两好」的标准已经合格了...12/29 19:19
2F：→ raymondseed :只有我想到棒球吗?12/29 23:13
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◆ From: 140.112.241.132
※ 编辑: shokanshorin 来自: 140.112.241.132 (04/15 17:35)
3F：推 liltwnboiz :GJ 04/15 20:57
※ liltwnboiz:转录至某隐形看板 04/15 20:57
4F：推 wuhoward :易富国 04/15 21:17
5F：推 ALegmontnick:done 04/15 22:35
※ 编辑: shokanshorin 来自: 140.112.241.132 (04/17 17:21)
6F：→ shokanshorin:小修第六题的积分式，请小板主重收 04/17 17:22
7F：推 ALegmontnick:done again 04/18 01:10
8F：→ shokanshorin:乾虾~~ 04/20 13:52