   Chapter 2.5, Problem 87E

Chapter
Section
Textbook Problem

In Exercises 85-97, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.87. If lim x → 2 f ( x ) = 3 and f(2) = 3 then lim x → 2 − f ( x ) = 3 .

To determine
Whether the statement is true or false with explanation.

Explanation

The given statement is,

If limx2f(x)=3 and f(2)=3 , then limx2f(x)=3

The function f has the right hand limit L as x approaches a from the right that is limxa+f(x)=L .

The function f has the left hand limit M as x approaches a from the left that is limxaf(x)=M .

If the value of limxaf(x) and limxa+f(x) is equal, then the function limxaf(x) exists.

For example,

f(x)={x3ifx<22x1ifx

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