verify-the-given-linear-approximation-at-a-0-then-determine-the-values-of-x-for-which-the-linear-a-3

Question

Verify the given linear approximation at $ a = 0. $ Then determine the values of $ x $ for which the linear approximation is accurate to within 0.1.
$ \sqrt [4]{1 + 2x} \approx 1 + \frac {1}{2}x $

Amrita Bhasin · Accepted Answer

okay. We know the four through of one plus two acts. Amino X zero gives us one there for the derivative would be 1/2 times one plus. If you plug in zero, we end up with 1/2. Therefore, we have the four through of one plus two. Axe equals one plus 1/2 axe. Therefore verifying this We know we have 0.1 is less than the four through of done pushed you axe on a swan. And this 1/2 acts, which is less than 0.1. Therefore we have 0.9 is less than four through of one plus two acts minus 1/2 axe. Just lost them 1.1. So we have. Why&#x27;s your 0.9? White is 1.1 to the values would be between the of 0.3689 and 0.6777

Problem

Verify the given linear approximation at $ a = 0.…

Problem 9 Medium Difficulty

Verify the given linear approximation at $ a = 0. $ Then determine the values of $ x $ for which the linear approximation is accurate to within 0.1.
$ \sqrt [4]{1 + 2x} \approx 1 + \frac {1}{2}x $

Answer

$-0.368<x<0.677$

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Caleb E.

Samuel H.

Michael J.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript