If limx →c f(x)=2 and limx →c^+ f(x)=2, then limx →c f(x)=2 . Justify your answer.

Name: Problem 71, Chapter 2: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-09-05T19:41:18-08:00
Duration: 1 min 49 s
Channel: Debasish Das
Description: If limx →c f(x)=2 and limx →c^+ f(x)=2, then limx →c f(x)=2 . Justify your answer.

step 1 Question number 71. You have to find the statement is true or false. It is given that limit X te

If limx →c f(x)=2 and limx →c^+ f(x)=2, then limx →c f(x)=2...

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Key Concepts

Two-Sided Limits

A two-sided limit at a point exists when the function approaches the same value from both the left and right sides. In other words, for the limit at a point to be defined, the left-hand limit and the right-hand limit must coincide. This central idea ensures consistency in the behavior of the function around the point.

One-Sided Limits

One-sided limits examine the behavior of a function as the variable approaches a specific point only from one side – either from the left (denoted as lim??c?) or from the right (denoted as lim??c?). They are essential in understanding situations where the function may not be defined on both sides of a point or might behave differently from different directions.

Relationship Between One-Sided and Two-Sided Limits

The existence of a two-sided limit is fundamentally linked to the one-sided limits. Specifically, the two-sided limit exists if and only if both the left-hand and right-hand limits exist and are equal. This relationship forms the backbone of justifying the overall limit from the behavior observed on each side of the point.

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