Taylor Polynomial Approximation

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Taylor Polynomial Approximation

Answer the following two questions:

Q1: Find the Taylor polynomial Tn (x) about a for the given function f (x). Then graph Tn (x) and f (x) on the same screen centered horizontally at x=a.

1. f (x) = ln x a = 1, n = 5

2. f (x) = tan x a = 0, n = 5

3. f (x) = tan x a = π/4, n = 4

4. f (x) = √x a = 4, n = 3

Q2:Find the Taylor polynomial of order 5 about 0 for the given function f (x) and use it to approximate f (0.25).


5. f (x) = sin 2x