   Chapter 2.3, 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

# Evaluate the limit, if it exists. lim h → 0 9 + h − 3 h

To determine

To evaluate: The value of limh09+h3h.

Explanation

Results used:

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).

Difference of square formula: (a2b2)=(a+b)(ab)

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

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

f(0)=9+030=930=330=00

The Quotient rule is not applicable for the function f(h) because the limit of the denominator is zero.

That is limh0(h)=0 (by limit law 8).

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

Calculation:

Let f(h)=9+h3h (1)

Take the limit h approaches to zero but h0.

Simplify f(h) by using elementary algebra as follows.

Take the conjugate of the numerator and multiply and divide by the conjugate

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