   Chapter 2.3, Problem 60E ### 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

# If lim x → 0 f ( x ) x 2 = 5 , find the following limits.(a) lim x → 0 f ( x ) (b) lim x → 0 f ( x ) x

(a)

To determine

To find: The limit of the function limx0f(x) when limx0f(x)x2=5.

Explanation

Limit Laws:

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

Limit law 9: limxaxn=an where n is a positive integer.

Given:

Suppose the limit of the function limx0f(x)x2 exists and equal to 5.

Calculation:

Obtain the limit of the function limx0f(x).

Multiply and divide the function by x2,

limx0f(x)=limx0(f(x)x2x2)=limx0(f(x)x2x2)=limx0(f(x)x2)limx0x2=(5)lim

(b)

To determine

To find: The limit of the function limx0f(x)x

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