Chapter 2.8, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The area of a triangle with sides of lengths *a* and *b* and contained angle

(a) If *a* = 2 cm, *b =* 3 cm, and *0* increases at a rate of 0.2 rad/ min, how fast is the area increasing when

(b) If *a* = 2 cm, *b* increases at a rate of 1.5 cm/min, and
*b* = 3 cm and

(c) If *a* increases at a rate of 2.5 cm/min, *b* increases at a rate of 1.5 cm/min, and
*a* = 2 cm, *b =* 3 cm, and

To determine

**a)**

**To find:**

How fast the area is increasing when

Explanation

**1. Formula used:**

i. Area of triangle

ii.

iii. Chain rule of differentiation:

**2. Given:**

a = 2 cm, b = 3 cm,

**3. Calculations:**

Consider

Differentiate both sides with respect to t

To determine

**b)**

**To find:**

How fast the area is increasing when b =3 and

To determine

**c)**

**To find:**

How fast the area is increasing when a= 2, b = 3 and

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