$\"\"$

The limit of the function is $\"\"$ .

Simplify the function $\"\"$ .

$\"\"$

Left hand limit $\"\"$ :

If $\"\"$ is close to $\"\"$ but smaller than $\"\"$ , then the denominator small negative number.

The function $\"\"$ approaches large positive number.

$\"\"$ .

Left hand limit $\"\"$ :

If $\"\"$ is close to $\"\"$ but larger than $\"\"$ , then the denominator small positive number.

The function $\"\"$ approaches large negative number.

$\"\"$ .

Left hand limit and right hand limit are not equal, so limit does not exist.

$\"\"$ does not exist.

$\"\"$

$\"\"$ does not exist.