Problem

Let $ f(x) = (x - 1)^2 g(x) = e^{-2x} $ and …

01:00

Problem 31 Easy Difficulty

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.
$ \frac {1}{9.98} \approx 0.1002 $

Answer

$f(9.98)=1 / 9.98 \approx 0.1-0.01(-0.02)=0.1+0.0002=0.1002$ so the approximation is reasonable.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Discussion

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Video Transcript

we know that f of X is one over acts. Therefore, we know that after prime of 10 plugging into the derivative may have turned to the night of two, which is negative 0.1 Therefore, 9.98 would be 0.1 plus negative 0.1 times Negative. 0.2 is 0.1002

Amrita B.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Top Calculus 1 / AB Educators

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Problem

Let $ f(x) = (x - 1)^2 g(x) = e^{-2x} $ and …

Problem 31 Easy Difficulty

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.
$ \frac {1}{9.98} \approx 0.1002 $

Answer

$f(9.98)=1 / 9.98 \approx 0.1-0.01(-0.02)=0.1+0.0002=0.1002$ so the approximation is reasonable.

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Kristen K.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Kristen K.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Problem

Let $ f(x) = (x - 1)^2 g(x) = e^{-2x} $ and …

Problem 31 Easy Difficulty

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.$ \frac {1}{9.98} \approx 0.1002 $

Answer

$f(9.98)=1 / 9.98 \approx 0.1-0.01(-0.02)=0.1+0.0002=0.1002$ so the approximation is reasonable.

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Kristen K.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Kristen K.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.
$ \frac {1}{9.98} \approx 0.1002 $