Question

We write$\underset{x\to a^{-}}{\lim }f\left(x\right)=L$and say that the ____ of $f\left(x\right)$as x approaches a from the ____ (left/right) is equal to ____. To find the left-hand limit, we try values for x that are ____ (less/greater) than a. A limit exists if and only if both the ____ -hand and ____-hand limits exist and are ____.

Short answer

The blank places will be filled up by left-hand limit, left, L, less, left, right and equalrespectively.

Step-by-step solution

Step 1. Given information.

The function of limit here given is,

$\underset{x\to a^{-}}{\lim }f\left(x\right)=L$

Step 2. Concept of one-sided limit.

If$\underset{x\to a^{-}}{\lim }f\left(x\right)=L$

Means, left hand limit of$f\left(x\right)$ is equal to L , as x approached from the left.

Where x is sufficiently close and less to .

Step 3. Conclusion.

By the definition,

We get the required answer.