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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Express the limit as a derivative and evaluate.

108. lim θ π / 3 cos θ 0.5 θ π / 3

To determine

To express: The limit as a derivative and obtain the value limθπ3cosθ0.5θπ3.

Explanation

Definition:

The derivative f(x) at a f(a)=limxaf(x)f(a)xa.

Calculation:

Compute limθπ3cosθ0.5θπ3.

Let f(x)=cosθ.

Substitute x=π3 in the above equation,

f(π3)=cosπ3=0.5

Obtain limθπ3cosθ0.5θπ3.

limθπ3cosθ0

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