The limit is $\"\"$ .

The above expression is in $\"\"$ form as $\"\"$ tends to zero. \ \

Thus, find the limit by L-Hospital rule.

L-Hospital rule:

Suppose $\"image\"$ or $\"image\"$ , then $\"image\"$

Apply L-Hospital rule. \ \

Here $\"\"$ and $\"\"$ .

$\"\"$ .

Differentiate on each side.

$\"\"$ .

Differentiate on each side.

$\"\"$ .

$\"\"$

$\"\"$ .

(b)

The limit is $\"\"$ .

Consider $\"\"$ .

To estimate the value of limit, construct a table with larger values of $\"\"$ by incresing rapidly.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

Observe the table results,

As the value of $\"\"$ increses then $\"\"$ value is close to zero. \ \

Thus, $\"\"$ .

(c)

The limit is $\"\"$ .

Apply squeeze theorem:

Suppose that $\"\"$ then

$\"\"$ , $\"\"$

As the range of $\"\"$ is $\"\"$ .

$\"\"$ .

Divide on each side by $\"\"$ .

$\"\"$

Apply infinite limits on each side.

$\"\"$

Since $\"\"$ .

Therefore, by squeeze theorem $\"\"$ .