(e) Find the first 4 terms of the Taylor series for the following functions (i) ln...

(e) Find the first 4 terms of the Taylor series for the following functions
(i) ln x centered at x0 = 1 . [8]
(ii) sin x centered at x0 =
π
4

Expert Solution

Colby Messinger answered 2 years ago

Find the first 6 terms of the Taylor Series for ln (x) around 1, that is...

Find the first 6 terms of the Taylor Series for ln (x) around 1, that is x = c = 1. Then use your results to calculate ln (3.52) and get the absolute error. I'm supposed to find the first 6 terms of the Taylor series for the functions ln (x ) centered at 1 that is x = c = 1.( or a=1). Then use the results to calculate ln (3.52) and get the absolute error.

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1. If f(x) = ln(x/4) -(a) Compute Taylor series for f at c = 4 -(b) Use Taylor series truncated after n-th term to compute f(8/3) for n = 1,.....5 -(c) Compare the values from above with the values of f(8/3) and plot the errors as a function of n -(d) Show that Taylor series for f(x) = ln(x/4) at c = 4 represents the function f for x element [4,5]

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