Chapter 14.4, Problem 41E

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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*/*h*^{2}, 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

Explanation

**Given:**

The body mass index

Where

The term

**Calculation:**

The given function is,

The linear approximation of the function

Find the partial derivative of the equation (1)with respect to

Find the partial derivative of the equation (1) with respect to

(b)

To determine

**To estimate:** The linear approximation of the body mass index

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