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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B(m, h) = m/h2, where m is the mass in kilograms and h is the height in meters.

(a) What is the linear approximation of B(m, h) for a child with mass 23 kg and height 1.10 m?

(b) If the child’s mass increases by 1 kg and height by 3 cm, use the linear approximation to estimate the new BMI. Compare with the actual new BMI.

(a)

To determine

To find: The linear approximation of the body mass index B(m,h)=mh2 at the mass m=23kg and the height h=1.10m .

Explanation

Given:

The body mass index B(m,h)=mh2 .

Where m is mass in kilograms.

The term h is height in meters.

Calculation:

The given function is, B(m,h)=mh2 (1)

The linear approximation of the function B(m,h)=mh2 at (23,1.10) is defined as,

B(23,1.10)B(23,1.10)+Bm(23,1.10)(m23)+Bh(23,1.10)(h1.1) (2)

Find the partial derivative of the equation (1)with respect to m at the point (23,1.10) ,

Bm(m,h)=1h2(1)=1h2Bm(23,1.10)=1(1.1)2=0.8264

Find the partial derivative of the equation (1) with respect to h at the point (23,1.10) ,

Bm(m,h)=m(2h3)=2mh3Bm(23,1

(b)

To determine

To estimate: The linear approximation of the body mass index B(m,h)=mh2 , use it to compare the actual BMI.

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 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-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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