   Chapter 2, Problem 7RE ### 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

# Find the limit. lim h → 0 ( h − 1 ) 3 + 1 h

To determine

To evaluate: The limit of the function limh0(h1)3+1h.

Explanation

Formula used:

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exist, then

Limit law 8: limxax=a

Direct substitution property:

If f is a polynomial or a rational function and a is in the domain of f, then limxaf(x)=f(a).

Fact 1:

If f(x)=g(x) when xa, then limxaf(x)=limxag(x), provided the limit exist.

Given:

Let f(h)=(h1)3+1h (1)

Note 1:

The direct substitution method is not applicable for the function f(h) as the function f(0) is in an indeterminate form when h=0.

f(0)=(01)3+10=1+10=00

Note 2:

The limit may be infinite or some finite value when both the numerator and the denominator approach to 0.”

Calculation:

By note 2, consider the limit h approaches to zero but h0.

Simplify f(h) by using elementary algebra

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