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A: Since multiple questions are asked I am answering first 3 subparts
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- Calculate the Taylor polynomial T3 centered at x = a for the given function and values of a andEstimate the accuracy of the 3th degree Taylor approximation, f(x) ≈T3(x), centered at x = a onthe given interval. 2) f(x) = ln(1 + 2x), a = 1, and [0.5,1.5]find the Taylor polynomial at x = a for the given function. f (x) = x ln(x), T4, a = 1Find the nth Taylor polynomial for the function f(x) = ln x, n = 4, centered at c = 2.
- Given: f(x) = ln(x + 2). 1. Find the third degree Taylor polynomial of f centered at 1. 2. Use the answer in number 1 to approximate the value of ln(3.05). Do not simplify.(a) Find the third-order Taylor polynomial generatedby y(x) = e−x about x = 1.(b) State the third-order error term.(c) Find an upper bound for the error term given|x| < 1Determine the fourth Taylor polynomial of f(x) = ln(1 - x)at x = 0, and use it to estimate ln(0.9).