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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Surface Area Use the result of Exercise 14 to order the planes in ascending order of their surface areas for a fixed region R in the xy-plane. Explain your ordering without doing any calculations.

(a) z 1 = 2 + x

(b) z 2 = 5

(c) z 3 = 10 5 x + 9 y

(d) z 3 = 3 + x 2 y

To determine
The order of planes in ascending order of their surface area by using the result of exercise 14 without doing any calculations. The planes are given below:

(a) z1=2+x

(b) z2=5

(c) z3=105x+9y

(d) z4=3+x2y

Explanation

Given:

The provided planes are:

(a) z1=2+x

(b) z2=5

(c) z3=105x+9y

(d) z4=3+x2y

The result of exercise 14 states that the area of a rectangular region in xy-plane is given as,

A=secθΔxΔy

Explanation:

It can be seen that area is directly proportional to the angle between the provided plane and the xy-plane according to the result of exercise 14, i.e., A=secθΔxΔy,. Hence, the greater the surface area the greater the the angle between the provided plane and the xy-plane

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Chapter 14 Solutions

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P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-66RECh-14 P-67RECh-14 P-68RECh-14 P-69RECh-14 P-70RECh-14 P-71RECh-14 P-72RECh-14 P-73RECh-14 P-74RECh-14 P-75RECh-14 P-76RECh-14 P-77RECh-14 P-78RECh-14 P-1PSCh-14 P-2PSCh-14 P-3PSCh-14 P-4PSCh-14 P-5PSCh-14 P-6PSCh-14 P-7PSCh-14 P-8PSCh-14 P-9PSCh-14 P-10PSCh-14 P-11PSCh-14 P-12PSCh-14 P-14PSCh-14 P-15PSCh-14 P-16PSCh-14 P-18PS

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