Using the function f(x)=ln(1+x) a. Find the 8 degree taylor polynomial centered at 0 and simplify. b. using...

60.1K

Verified Solution

Question

Advance Math

Using the function f(x)=ln(1+x)
a. Find the 8 degree taylor polynomial centered at 0 andsimplify.
b. using your 8th degree taylor polynomial and taylorsinequality, find the magnitude of the maximum possible error on[0,0.1]
c.approximate ln(1.1) using your 8th degree taylor polynomial.what is the actual error? is it smaller than your estimatederror?Round answer to enough decimal places so you candetermine.
d. create a plot of the function f(x)=ln(1+x) along with yourtaylor polynomial. Based on the plot what appears to be theinterval of convergence? explain.

Answer & Explanation Solved by verified expert

3.9 Ratings (597 Votes)

a The Taylor series of a function fx at x 0 is called the Maclaurin series of the function which isgiven byNow our given function is fx ln1x so wehaveSo we haveSimplifying we getNow we need to take the 8th degree Maclaurin series so we takeupto 8 terms of the above series Hence we havewhich See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member