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Graphing Taylor polynomials Consider the function f(x) =

Chapter 1, Problem 50RE

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QUESTION:

Graphing Taylor polynomials  Consider the function \(f(x)=(1+x)^{-4}\).

a. Find the Taylor polynomials \(p_0,\ p_1,\ p_2\), and \(p_3\) centered at 0.

b. Use a graphing utility to plot the Taylor polynomials and f for -1 < x < 1.

c. For each Taylor polynomial, give the interval on which its graph appears indistinguishable from the graph of f.

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QUESTION:

Graphing Taylor polynomials  Consider the function \(f(x)=(1+x)^{-4}\).

a. Find the Taylor polynomials \(p_0,\ p_1,\ p_2\), and \(p_3\) centered at 0.

b. Use a graphing utility to plot the Taylor polynomials and f for -1 < x < 1.

c. For each Taylor polynomial, give the interval on which its graph appears indistinguishable from the graph of f.

ANSWER:

Solution 50RE

Step 1:

Given that

f(x) = (1+ x)−4

Step2:

To find

a. Find the Taylor polynomials p0, p1, p2, centered at 0.

b. Use a graphing utility to plot the Taylor polynomials and f for −1<x<1.

c. For each Taylor polynomial, give the interval on which its graph appears indistinguishable from the graph of

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