Estimating Limits from Graphs

Where Limits Do Not Exist

If the limit is out of bounds or is an asymptote, it is considered unbounded and does not exist.

If the limit is not connected from the left side and the right side, then it does not exist.

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Where Limits Do Not Connect

Limits only exist when the function connects from both sides.

This can be checked by computing the limit as it approaches from the left and approaching to the right.

Example:

The limit of $f(x)$ as $x$ approaches $2$ from the negative or left side is 5,

${\lim }_{x\to 2^{-}}f(x)=5$ while the limit of $f(x)$ as $x$ approaches $2$ from the positive or right side is 1,

$$\underset{x\to 2^{+}}{\lim }f(x)=1$$

therefore the limit does not exist.