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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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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