   Chapter 2.3, Problem 13E ### 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 x → 5 x 2 − 5 x + 6 x − 5

To determine

To evaluate: The limit of the function limx5x25x+6x5.

Explanation

Limit Laws:

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

Limit law 2: limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 7: limxac=c

Limit law 8: limxax=a

Reason:

The limit of the denominator is zero.

limx5(x5)=limx5(x)limx5(5) (by limit law 2)=(5)(5) (by limit law 8 and 7)=0

The limit of the numerator is 6

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