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Chapter 14: Q. 55 (page 883)

In Problems 53-56, use the properties of limits and the facts that

limx鈫�0sinxx=1limx鈫�0cosx-1x=1limx鈫�0sinx=0limx鈫�0cosx=1

limx鈫�03sinx+cosx-14x

Short Answer

Expert verified

The limit equals34

Step by step solution

01

Given information

Given functionlimx鈫�03sinx+cosx-14x

02

Splitting the expression and calculatinglimx→03sinx+cosx-14x=limx→03sinx4x+cosx-14xlimx→03sinx+cosx-14x=limx→03sinx4x+cosx-14xlimx→03sinx+cosx-14x=limx→034·sinxx+14·cosx-1xlimx→03sinx+cosx-14x=limx→034·sinxx+14·cosx-1xlimx→03sinx+cosx-14x=limx→034·limx→0sinxx+limx→014·limx→0cosx-1xlimx→03sinx+cosx-14x=34·1+14·0limx→03sinx+cosx-14x=34

The limit is34

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