Answering worksheet calculus 2 help

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MTH 174 Exam2 take home Must show all work. Write clearly to receive full credits. NVCC Academic Dishonesty APPLIED. Follow instruction – Deduct10 points for not follow instruction All questions must answer in ORDER Separate each questions by draw a line or start a new page Only write on one-sided of the page Must use blank printing paper (NO line paper) DUE Tuesday July 25, 2017 no later than 9AM NO EXCEPTION DID YOU READ THE INSTRUCTION ABOVE? Z 1 1. Evaluate the integral dx 2 (x + 1)(x − 3) 2. Determine whether the series converge or diverge. Identify which method that you used. (a) (b) (c) ∞ X (−1)n n=1 ∞ X 3n n2 (−1)n+1 e−n n3 n=1 ∞ X 2 nn (−1) n 2 n=1 ∞ X 1 n=1 n ln(n) ∞ X sin(n) + 1 (e) n2 n=1 (d) 3. Find all possible p such that Z ∞ 2 1 dx converge. x(ln x)p 4. TRUE or FALSE? If true state a theorem to justify your conclusion; if false, then give a counterexample. (a) If lim an = 0 , then n−>∞ (b) (c) (d) (e) If If If If a a a a sequence sequence sequence sequence an an an an P an converge. P converge, then an converge. P diverge, then an diverge. P converge, then an diverge. P diverge, then an converge. 5. Find a taylor series polynomial of degree 5th for f (x) = 1 center c = 2. 2x + 1 Find the upper bound error on the interval [1, 4] 6. Find a convergence interval of f (x), f 0 (x) and where f (x) = ∞ X (−1)n n=1 Z f (x)dx 3n (x + 2)n n2 SERIOUSLY, DID YOU READ THE INSTRUCTION ABOVE? 1
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HiPlease check the attached file for details, let me know if you have any questions,in case that you need, I also attached pdf file, thank you. James

1.

1
A
Bx  C

 2
( x  1)( x  3) ( x  3) ( x  1)
2

1
( Bx  C )
 A 2
( x  3)
( x  1)
( x  1)
2

Let x =3,
A = 1/10

1
1 ( Bx  C )
  2
( x  3)
( x  1) 10 ( x  1)
2

x2  1
 Bx 2  (3B  C ) x  3C
10
1
B
10
3
C
10

1




1
1
1
x3
dx   (
 2
)dx
( x  1)( x  3)
10
( x  3) ( x  1)
2

1
1
3
ln | x  3 |  ln( x 2  1)  tan 1 x  C
10
20
10

2. a) limit of an
Diverges. Because
|an| = 3n/n2 diverges to infinity at n = infinity.
b) Ratio test
Converges . Since

an1
e  n1 (n  1) 3
 lim
n    a
n   
e n n 3
n
lim

1
 lim e 1 (1  ) 3
n   
n
 1/ e  1
c)Ratio test.
Converges. Since

an1
2  ( n1) ( n  1) 2
 lim
n    a
n   
2 n n 2
n
lim

1
 lim 2 1 (1  ) 2
n   
n
 1/ 2  1
d) Integration test.
Diverges. Since


1

 x ln x dx  ln(ln

x)

1


1

does not converge.
e) Comparison test.
Converges. Since

|

sin n  1 1
1
2
| 2  2  2
2
n
n
n
n

and


2

n
n 1

2

Converges.

3.

1

 x(ln x)

p

dx  

1
d ln x
(ln x) p

 ln ln x, p  1

1
 1
p 1
,
p

1
1  p (ln x)
For the integral converge, it needs to require that p-1>0, or p>1. Then the integral converge to

1
(...


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