The meaning of lim x → 1 − f ( x ) = 3 and lim x → 1 + f ( x ) = 7 and the existence of lim x → 1 f ( x ) .

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 2E
To determine

To explain: The meaning of limx→1−f(x)=3 and limx→1+f(x)=7 and the existence of limx→1f(x).

Expert Solution

Explanation of Solution

The meaning of limx1f(x)=3 is, as the values of x gets more closer to 1 from the left that is x<1, the value of f(x) arbitrarily approaches 3.

The meaning of limx1+f(x)=7 is, as the values of x gets more closer to 1 from the right that is x>1, the value of f(x) arbitrarily approaches 7.

The equation limx1f(x)=L does not exist since the left-hand limit and right-hand limit are not the same.

Recall the definition of the limit of a function that the limit exists when the right hand limit and the left hand limit are the same.

Since, the left-hand limit is 3 and the right hand limit is 7, limx1f(x) does not exist.

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