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The circumference of a sphere was measured to be …

10:50

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Problem 34 Hard Difficulty

The radius of a circular disk is given as $ 24 cm $ with a maximum error in measurement of $ 0.2 cm. $
(a) Use differentials to estimate the maximum error in the calculated area of the disk.
(b) What is the relative error? What is the percentage error?


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

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Differentiation

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Derivatives - Intro

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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44:57

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
Problem 17
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Problem 22
Problem 23
Problem 24
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Problem 30
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Problem 32
Problem 33
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Problem 36
Problem 37
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Problem 43
Problem 44

Video Transcript

Okay. The driven of six X squared is 12 ax. Therefore, we know the maximum error 12 times, 30 times 0.1 gives us 36 centimeters squared. Therefore, relative errors. The area over the surface area therefore 36 divided by six times 30 squared gives 0.0 6/7 on then this ring as a percentage times 100 would be 0.67% for part B. We know that if us his pyre square that s prime of our In other words, the derivative would be two pi r. Therefore, we have to pie times 24 times changing our gives 9.6 pie centimeters squared.

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
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Video Thumbnail

04:40

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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.

Video Thumbnail

44:57

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