   Chapter 2, Problem 2RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. lim x → 1 x 2 − 6 x − 7 x 2 + 5 x − 6 = lim x → 1 ( x 2 + 6 x − 7 ) lim x → 1 ( x 2 + 5 x − 6 )

To determine

Whether the statement, limx1(x2+6x7x2+5x6)=limx1(x2+6x7)limx1(x2+5x6) is true or false.

Explanation

Quotient Law: Suppose that the limits limxaf(x) and limxag(x) exist.

Then limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0

Reason:

Let the function Q(x)=f(x)g(x) where f(x)=x2+6x7 and g(x)=x2+5x6.

Then, by the Quotient Law, the given statement is true only if the limit of the denominator Q(x) is not equal to zero as x approaches 1

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