   Chapter 3.10, Problem 19E ### 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.19. y = x2 – 4x. x = 3, ∆x = 0.5

To determine

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

Explanation

Given:

The function is y=x24x. The value x=3 and Δx=0.5

Calculation:

Obtain the value of Δy.

Consider the function f(x)=x24x.

Δy=f(x+Δx)f(x)

Substitute the value x=3 and Δx=0.5,

Δy=f(3+0.5)f(3)=f(3.5)f(3)=[(3.5)24(3.5)][324(3)]=[12.514]

Simplify the terms,

Δy=1.75(3)=1.75+3=1.25

Thus, the value Δy=1.25.

Obtain the value of dy.

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

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