   Chapter 3.3, Problem 45E ### 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 θ → 0 sin θ θ + tan θ

To determine

To find: The limit of limθ0sinθθ+tanθ.

Explanation

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exist. Then

(1) limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

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

(3) limxa[f(x)g(x)]=limxaf(x)limxag(x) if limxag(x)0

Result used:

The value of limθ0sinθθ is 1.

Calculation:

Compute limθ0sinθθ+tanθ.

Divide the numerator and the denominator by θ,

limθ0sinθθ+tanθ=limθ0sinθθθ+tanθθ=limθ0sinθθθθ+tanθθ=limθ0sinθθ1+sinθθcosθ       [

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 