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Problem

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

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Problem 31 Easy Difficulty

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


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Related Topics

Derivatives

Differentiation

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In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Watch More Solved Questions in Chapter 3

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Problem 16
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Problem 28
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Problem 44

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

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Calculus: Early Transcendentals

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Video Thumbnail

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