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  3. using the function f(x)=ln(1+x) a. find the 8 degr

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

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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
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