   Chapter 10.1, Problem 70E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

What is wrong with the following statement? “Because f ( a ) isdefined, lim x → a f ( x ) exists.” Illustrate your claim with an example.

To determine

The reason why the statement, “Because f(a) is defined, limxaf(x) exists” is wrong and to provide an example for it.

Explanation

Given information:

The given statement is, “Because f(a) is defined, limxaf(x) exists”.

The example that is used to make the statement wrong is as follows:

Consider the expression, limx1x2+2x+1x+1

Where, f(x)=x2+2x+1x+1

Substitute x=0 in f(x)=x2+2x+1x+1:

f(0)=02+2(0)+10+1=1

Here f(0) exist.

Make the table for the corresponding values of f(x) by substituting random values of x approaching to 1 from left and right.

Then, the table is as follows:

When x is approaching to 1 from the left,

 x −1.1 −1.01 −1.001 −1.0001 −1 f(x) −0

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