100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Mth 1002 Powers Series of Functions from Known Function $11.99   Add to cart
Quickly navigate to
Preview
  2.  
  3. Florida Institute Of Technology
  4.  
  5. MTH 1002 Calculus 2

Other

Mth 1002 Powers Series of Functions from Known Function

 1 view  0 purchase

This is a comprehensive and detailed practice material on Powers Series of Functions from Known Function for Mth 1002.

Preview 1 out of 2  pages

Document information

  • October 16, 2024
  • 2
  • 2020/2021
  • Other
  • Unknown

Subjects

Written for

All documents for this subject (3)

Seller

avatar-seller
anyiamgeorge19

Reviews received

Content preview

CALCULUS 2 NAME: ________________________________

LAB 31 11.10 TAYLOR & MACLAURIN SERIES Lab Time: ____________ Date: __________

Basic Definitions:

a
Using the known Geometric Series Formula:  ar
n0
n
 a  ar  ar 2  ar 3  ... 
1 r
which holds when r  1,

new series formulas can be created by a suitable replacement of terms.


a
a  ar  ar  ar  ...  ar and making the replacements a 1
2 3 n
1. Using the formula
1 r n0


and r  x , create a new series formula for 1 and give its interval of converegence.
1 x


1
1  1x  1x 2  1x 3  ...  1x n
1 x n 0



1
1  x  x  x  ...  x
2 3 n

1 x n 0


r 1  x 1   1  x 1
Interval :   1,1


1
2. Replace the x-term in your formula from the previous problem with   x to create a formula for .
1 x


1 1
 1   x    x  2   x 3  ...    x  n
1  x 1   x  n 0

1  x  x 2  x 3  ...    1 x n
n

n0



3. Integrate your formula from the previous problem with term-by-term to create a formula for ln  x  1 .
(Don’t forget to find the constant “C” by plugging in x 0 )


ln x  1 x 11 dx  1  x  x2  x3  ... dx C  x   1
2 x 2  13 x3  1
4 x 4  ...


ln  x  1 C  x  1
2
x 2  13 x3  1
4
x 4  ...
x  0  ln 0  1 C  0  0  13 0 
3 2
1
2
1
4 04  ...
ln 1 C  0  0  0  0  ...
0 C
 ln x 1  0  x  1
2
2 3
x  13 x  1
4
4
x  ...

x4  ...    1n
n1
So : ln  x  1  x  1
2
2
x  x  1
3
3 1
4 xn
n 1



1
4. Replace the x-term in the formula 1  x  x 2  x3  ...  x n
1 x n 0

1
with   x2  to create a formula for .
1 x 2

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller anyiamgeorge19. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $11.99. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

84669 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$11.99
  • (0)
  Add to cart