Question

Example 47. 1. Find an expression for the maximum error when the first 4 terms of the Maclaurin series for the function $$f(x)=\frac{1}{1+ax},$$ a a positive constant, are used to approximate the function on the interval $$0 \leq x \leq 0.1.$$ 2. What is the largest value of a if the maximum error must be less than or equal to $$10^{-8}?$$

Name: example 47 1 find an expression for the maximum error when the first 4 terms of the maclaurin series for the function fxfrac11ax a a positive constant are used to approximate the function on 46863
Uploaded: 2020-09-05T01:04:20-08:00
Duration: 6 min 14 s
Channel: Carlos Pinilla
Description: example 47 1 find an expression for the maximum error when the first 4 terms of the maclaurin series for the function fxfrac11ax a a positive constant are used to approximate the function on 46863

          Example 47. 1. Find an expression for the maximum error when the first 4 terms of the Maclaurin series for the function
$$f(x)=\frac{1}{1+ax},$$
a a positive constant,
are used to approximate the function on the interval $$0 \leq x \leq 0.1.$$
2. What is the largest value of a if the maximum error must be less than or equal to $$10^{-8}?$$

$example 47 1 find an expression for the maximum error when the first 4 terms of the maclaurin series for the function fxfrac11ax a a positive constant are used to approximate the function on 46863$

Added by Robert L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carlos Pinilla

09/05/2020

Step 1

1$. Then, we need to find the largest value of $a$ if the maximum error must be less than or equal to $10^{-8}$. First, let's find the Maclaurin series for $f(x) = \frac{1}{1+ax}$. We know the geometric series formula: $\frac{1}{1-r} = 1 + r + r^2 + r^3 + \dots$ Show more…

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Example 47. 1. Find an expression for the maximum error when the first 4 terms of the Maclaurin series for the function $$f(x)=\frac{1}{1+ax},$$ a a positive constant, are used to approximate the function on the interval $$0 \leq x \leq 0.1.$$ 2. What is the largest value of a if the maximum error must be less than or equal to $$10^{-8}?$$