   Chapter 3.3, Problem 43E ### 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 x → 0 sin 3 x 5 x 3 − 4 x

To determine

To find: The limit of limx0sin3x5x34x.

Explanation

Limit Law:

Suppose that the limits limxaf(x) and limxag(x) exist, then

limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0 (1)

Result used:

The value of limθ0sinθθ is 1.

Calculation:

Compute limx0sin3x5x34x.

Divide the numerator and the denominator by 3,

limx0sin3x5x34x=limx0(33sin3x5x34x)=limx0(3sin3x3x(

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