Find the second-degree Taylor polynomial of f(x)=ln(1+sinx) centered at x=0.

Expert Solution

milcah answered 1 year ago

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

Using the function f(x)=ln(1+x) a. Find the 8 degree taylor polynomial centered at 0 and simplify. b. using your 8th degree taylor polynomial and taylors inequality, 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 estimated error?Round answer to enough decimal places so you can determine. d. create a plot of the function f(x)=ln(1+x) along with your taylor polynomial. Based on...

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find the taylor polynomial T5 of f(x) = e^x sinx with the center c=0 hint: e^x = 1 + x + x^2/2! + x^3/3! + ..., sinx=x - x^3/3! + x^5/5! -...

Find the Taylor series for f(x)= ln(2+x) centered at x=0 and compute its interval of convergence....

Find the Taylor series for f(x)= ln(2+x) centered at x=0 and compute its interval of convergence. Show all work and use proper notation.

(a) Determine the Taylor Series centered at a = 1 for the function f(x) = ln...

(a) Determine the Taylor Series centered at a = 1 for the function f(x) = ln x. (b) Determine the interval of convergence for this Taylor Series. (c) Determine the number n of terms required to estimate the value of ln(2) to within Epsilon = 0.0001. Can you please help me solve it step by step.

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Represent f(x)=sinx as the sum of its Taylor series centered at x=pi/6. Find the radius of...

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Let f(x) = 1 + x − x2 +ex-1. (a) Find the second Taylor polynomial T2(x)...

Let f(x) = 1 + x − x2 +ex-1. (a) Find the second Taylor polynomial T2(x) for f(x) based at b = 1. b) Find (and justify) an error bound for |f(x) − T2(x)| on the interval [0.9, 1.1]. The f(x) - T2(x) is absolute value. Please answer both questions cause it will be hard to post them separately.

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