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Chapter 1: Q. 83 (page 136)

Use the Squeeze Theorem to find each of the limits in Exercises. Explain exactly how the Squeeze Theorem applies in each case.

limx鈫�1(x-1)cos1x-1

Short Answer

Expert verified

The limit of the equationlimx鈫�1(x-1)cos1x-1is 0

Step by step solution

01

Step 1. Given Information:

limx鈫�1(x-1)cos1x-1

02

Step 2. Applying Squeeze theorem on the limit:

By applying the Squeeze theorem;

Rangeofcos1x-1"orcosx"is[-1,1]-1鈮�cos1x-1鈮�1Nowmultiplying(x-1)onallside;-(x-1)鈮�(x-1)cos1x-1鈮�x-1-x+1鈮�(x-1)cos1x-1鈮�x-1Applyinglimitsonallsideasx鈫�1;limx鈫�1-x+1鈮�limx鈫�1(x-1)cos1x-1鈮�limx鈫�1x-1-1+1鈮�(1-1)cos11-1鈮�1-10鈮�0(cos0)鈮�00鈮�0鈮�0so,limx鈫�1(x-1)cos1x-1=0
03

Step 3. Graph Representation: 

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