Problem

The circumference of a sphere was measured to be …

10:50

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?

Answer

(a) 9.6$\pi$ square $\mathrm{cm}$
(b) 0.017 or 1.7$\%$

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Discussion

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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.

Amrita B.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Samuel H.

University of Nottingham

Joseph L.

Boston College