   Chapter 3.10, Problem 21E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Compute ∆y and dy for the given values of x and dx = ∆x. Then sketch a diagram like Figure 5 showing the line segments with lengths dx, dy, and ∆y.21. y = x − 2 ,   x = 3 ,   Δ x = 0.8

To determine

To compute: The value Δy and dy for the given values of x and dx=Δx. Sketch the line segment with lengths dy,Δy and dx.

Explanation

Given:

The function is y=x2. The value x=3 and Δx=0.8

Calculation:

Obtain the value of Δy.

Consider the function f(x)=x2.

Δy=f(x+Δx)f(x)

Substitute the value x=3 and Δx=0.8,

Δy=f(3+0.8)f(3)=f(3.8)f(3)=3.8232=1.81

Simplify the terms,

Δy=1.3411=0.3410.34

Thus, the value Δy0.34.

Obtain the value of dy.

Note that, the differential is dy=f(x)dx.

The derivative of the function f(x) is computed as follows,

f(x)=ddx(x2)=12(x2)121

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