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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

Find the limit.

lim x π / 4 1 tan x sin x cos x

To determine

To find: The limit of limxπ41tanxsinxcosx.

Explanation

Calculation:

Compute limxπ41tanxsinxcosx.

Divide the numerator and denominator by cosx5,

limxπ41tanxsinxcosx=limxπ41tanxsinxcosxcosxcosx=limxπ4(1sinxcosx)cosx(sinxcosx)cosx    (Qtanx=sinxcosx)=limxπ4(cosxsinxcosx)cosx(sinxcosx)cosx=limxπ4cosxsinx(sinxcosx)cosx

Simplify further and obtain the limit as follows

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