作者nosignal90 (NoSignal)
看板trans_math
标题[考古] 98市北教
时间Sun Jun 5 22:02:27 2011
各位好，刚才把这份写完了，想请各位帮忙看看答案对不对>_<（好紧张喔）
1.
2 2
Let f(x)= x a , if x ≦2 For what value of a is f continuous at 2 ?
( 1-a )x , if x >2
1
my answer is a = -1 or -----
2
2. 3
x - 4 x
Find H'(2) given that H(x)= ∫ ------------ dt
2x 1 + √t
my answer is 20/3.
3.
x
calculate ∫xe dx
x x
my answer is xe - e + c
4. 3
tan x
calculate ∫ ----------- dx
______
√sec x
1 1 _____ 3 1
my answer is ----- ( ----- (√secx ) + ---------- ) + c
2 3 ______
√ secx
5.
2 dx
evaluate ∫ ------
-1 3
x
my answer is 3/8
6.
_______
2 √4 - x^2 4
Evalute the integral ∫ ∫ ∫ dzdydx
-2 - √4 - x^2 x^2 + y^2
my answer is 8pi
7.
Determine the convergence or divergence of the series
∞ 1
Σ -------------- my answer is convergence.
n =1 _________
√ 3
n + 2n
这题我的过程是这样的
n^3 +2n > n^3
_______ ____
→ √n^3 +2n > √n^3
1 1
------------- < --------
_______ ____
√n^3 +2n √n^3
取 1 / ((n^3)^1/2) 为bn，并由p级数证出是con.
所以原级数convergence
(写级数的证明题都不太晓得过程是否完善...Orz)
嗯，就先这样，麻烦各位了，谢谢：）
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