   Chapter 2.R, Problem 85E

Chapter
Section
Textbook Problem

# A window has the shape of a square surmounted by a semicircle. The base of the window is measured as having width 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.

To determine

To estimate:

Maximum possible error (dA) in computing the area of the window

Explanation

1. Concept:

Use of Differentials, Derivative of function

2. Formula:

i. Differential Formula:

dy=f'x dx

ii. Area of Square:

A= a2, where a=lenght of side

iii. Area of Semicircle:

A= 12 π a22, where a=diameter of semicircle

iv. Power rule:

ddxxn=n xn-1

3. Given:

a=60 cm, error=0.1 cm

4. Calculation:

Assume,  a=lenght of side

Then area of square is

Area= a2

By using standard formula area of semicircle is

Area= 12 π a22

Let A be the total area of the window

Therefore, A=Area of square+Area of sem

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