find-the-linear-approximation-of-the-function-gx-sqrt-31-x-at-a-0-and-use-it-to-approximate-the-numb

Name: find the linear approximation of the function gx sqrt 31 x at a 0 and use it to approximate the numb
Uploaded: 2019-11-03
Duration: 1 min 19 s
Channel: Numerade
Description: Find the linear approximation of the function $ g(x) = \sqrt [3]{1 + x} $ at $ a = 0 $ and use it to approximate the numbers $ \sqrt [3]{0.95} $ and $ \sqrt [3]{1.1}. $ Illustrate by graphing $ g $ and the tangent line.

Question

Find the linear approximation of the function $ g(x) = \sqrt [3]{1 + x} $ at $ a = 0 $ and use it to approximate the numbers $ \sqrt [3]{0.95} $ and $ \sqrt [3]{1.1}. $ Illustrate by graphing $ g $ and the tangent line.

Amrita Bhasin · Accepted Answer

Okay, Jim zero is the cube root of one plus zero, which is one therefore, G prime of acts is 1/3 times. Now we&#x27;re playing in zero. So one plus zero to the negative to over three simplifies to 1/3 plug into the blender or ization formula with sequels one plus 1/3 axe. So now we have one plus X equals 0.95 they&#x27;re for ox equals negative 0.5 Therefore, we have one plus 1/3 times negative 0.5 0.9833 You know The cube root of 1.11 plus X is 1.1 an ax 0.11 plus 1/3 time&#x27;s Your 0.1 is one point 1.3 three.

Problem

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

Problem 6 Medium Difficulty

Find the linear approximation of the function $ g(x) = \sqrt [3]{1 + x} $ at $ a = 0 $ and use it to approximate the numbers $ \sqrt [3]{0.95} $ and $ \sqrt [3]{1.1}. $ Illustrate by graphing $ g $ and the tangent line.

Answer

$L(x)=1+\frac{1}{3} x, \quad \sqrt[3]{0.95} \approx 0.9833, \quad \sqrt[3]{1.1} \approx 1.033$

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Kayleah T.

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