# The meaning of lim x → 2 f ( x ) = 5 and check whether this statement is true for f ( 2 ) = 3 or not. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.2, Problem 1E
To determine

## To explain: The meaning of limx→2f(x)=5 and check whether this statement is true for f(2)=3 or not.

Expert Solution

The meaning of limx2f(x)=5 is, as x approaches 2, f (x) gets closer and closer to 5.

The statement is true.

### Explanation of Solution

Suppose the function f(x) is defined for all x near 2 but not exactly at x=2.

The limx2f(x)=5 exists if f(x) gets arbitrarily close to 5 as x gets sufficiently closer (but not equal) to 2 from both sides of 2.

Therefore, the limit of the function f(x) exists and equal to 5 when x approaches 2 and it can be written as limx2f(x)=5.

Possibly this statement is true for f(2)=3 as the limit depends upon the functional values near to 2 but not exactly at 2.

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