各位好，剛才把這份寫完了，想請各位幫忙看看答案對不對>_<（好緊張喔）
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
這題我的過程是這樣的
n^3 +2n > n^3
_______ ____
→ √n^3 +2n > √n^3
1 1
------------- < --------
_______ ____
√n^3 +2n √n^3
取 1 / ((n^3)^1/2) 為bn，並由p級數証出是con.
所以原級數convergence
(寫級數的證明題都不太曉得過程是否完善...Orz)
嗯，就先這樣，麻煩各位了，謝謝：）
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.231.144.163
※ 編輯: nosignal90 來自: 61.228.44.235 (06/06 09:36)