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Chapter 1: Q. 81 (page 89)

Prove that for all x within 0.01 of the value x = 1, the quantity 1x-12 is greater than 10, 000. What does this have to do with

limx鈫�11x-12?

Short Answer

Expert verified

The given statement is proved. The value of the limitlimx鈫�11x-12=鈭�.

Step by step solution

01

Step 1. Given Information.   

The given quantity is 1x-12.

02

Step 2. Prove.   

Let the function isf(x)=1x-12.

Take the limit of the above function asx鈫�0.01:

limx鈫�0.01f(x)=limx鈫�0.011x-12limx鈫�0.01f(x)=10.01-12limx鈫�0.01f(x)=1.02

Now, take the limit of the above function as x鈫�1:

limx鈫�1f(x)=limx鈫�11x-12limx鈫�1f(x)=11-12limx鈫�1f(x)=10limx鈫�1f(x)=鈭�

Therefore, the quantity1x-12is greater than10,000.

03

Step 3. Finding the limit.

Let's find the limit:

limx鈫�1f(x)=limx鈫�11x-12limx鈫�1f(x)=11-12limx鈫�1f(x)=10limx鈫�1f(x)=鈭�

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