# Calculus 2

1. Evaluate each improper integral or show that it diverges.

(1)  +

Don't use plagiarized sources. Get Your Custom Essay on
Calculus 2
Just from \$13/Page

1 x

dx

(2)  +

− ++ 22 2

xx

dx

(3)  −

2

0 2)1( x

dx

(4)  −

e

xx

dx

1 2 )(ln1

2. For what values of k does the integral )( )(

ab ax

dxb

a k 

−  converge and for what

values does it diverge?

3. Calculate the area of the following regions.

(1) The region bounded by xx eyey −== , and 1=x .

(2) The region bounded by )cos1(2  += a (a>0).

4. Sketch and find the area of the region bounded by  cos3= and

 cos1+= .

5. Find the volume of the solids generated by revolving about the x-axis the

region bounded by 02 =− yx and the parabola xy 42 = .

6. Find the length of 3

4 xy = between x = 1/3 and x = 5.

7. Find the length of the curve 41;12,23 32 −=+= ttytx .

8. Fill the blanks.

(1) If  

=

 

  

 −

1 2

3

n

n

n

x a converges at 0=x , then it __________ (converges, diverges)

at 5=x .

(2) If 2lim 1

= +

→ n

n

n c

c , then the convergence radius of 

=0

2

n

n n xc is _______.

9. Find the convergence set of each series.

(1)  

= +1 2

1

2

n

n n

x n

(2)  

=

−+

1 3

)1(3

n

n

n

n

x

10. Find the sum function of the power series.

(1)  

=1n

n nx

(2)  

=

− −1

12

)11(, 12n

n

x n

x , and the sum of 

= −1 2)12(

1

n n

n .

11. Find the Taylor series of x

xf +

= 3

1 )( in )2( −x .

12. Recall that td t

x x

 −

= 0 2

1

1 arcsin ,

and find the first four nonzero terms in the Maclaurin series for xarcsin .

Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Writall
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Nursing
Thank you!!
Customer 454959, February 6th, 2022
Nursing
Thank you!
Customer 454959, February 6th, 2022
Criminal Justice
great paper. came fast and exactly what I needed
Customer 455099, November 13th, 2021
Criminal Justice
Absolutely LOVE the essay I received. I really appreciate it so much.
Customer 454561, February 16th, 2021
Sports
Great stuff
Customer 455371, June 26th, 2022
Accounting
Outstanding!!
Customer 454639, March 30th, 2021
Psychology
Greater than anticipated. Thanks for the start.
Customer 454569, November 8th, 2020
Social Work and Human Services
I love how the writer pays attention to detail, this is allowing me great opportunity to learn even more from his writing styles!!
Customer 453933, October 1st, 2020
Great work!
Customer 455105, May 10th, 2022
Other
Great work as always
Customer 454983, January 28th, 2022
This is exactly what I was looking for and you all helped me out so much! Thank you!!!!!
Customer 454769, June 16th, 2021
Film & Theater studies
Amazing job. Thank you
Customer 454983, November 24th, 2021
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend