   Chapter 2.9, Problem 22E

Chapter
Section
Textbook Problem

# 19-22 Compute Δ y and dy for the given values of x and d x = Δ x . Then sketch a diagram like Figure 5 showing the line segments with lengths dx, dy, and Δ y . y = x 3 ,   x = 1 ,   Δ x = 0.5

To determine

To compute:

y and dy for the given values of x and dx=x and sketch a diagram showing the line segment dx, dy and y

Explanation

1) Formula:

i. y=fx+x-f(x)

ii. dy=f'xdx

2) Given:

y=fx=x-x3

3) Calculation:

By using formula,

y=fx+x-f(x)

Since, x=1 and x=0.5

y=f1+0.5-f(1)

y=f1.5-f(1)

Since, y=fx=x3

y=1.53-13=3.375-1=2.375

y= Therefore,  y=2

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