   Chapter 2.4, Problem 11E

Chapter
Section
Textbook Problem

A machinist is required to manufacture a circular metal disk with area 1000 cm2.(a) What radius produces such a disk?(b) If the machinist is allowed an error tolerance of ±5 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?(c) In terms of the ε δ definition of lim x → a f ( x ) = L , what is x? What is f(x)? What is a? What is L? What value of ε is given? What is the corresponding value of δ?

(a)

To determine

To find: The radius of the disk.

Explanation

Result used:

The area of the circle is A=πr2, where r is the radius.

Calculation:

Given the area of the disk A=1000cm2 (1)

The area of the circle is A=πr2 (2)

From equation (1) and (2)

1000=πr

(b)

To determine

To find: The ideal radius of the disk.

(c)

To determine

To explain: The terms in ε,δ definition of limxaf(x)=L.

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