(1)

Step 1:

The expression is .

Consider .

Apply logarithm on each side.

.

Apply limits on each side as .

.

Step 2: 

L-Hospital rule: 

Suppose or , then

Apply L-Hospital rule.

Multiply numerator and denominator by .

As then .

.

.

Solution:

.

(b)

Step 1:

The expression is .

.

Step 2:

L-Hospital rule:

Suppose or , then  

Apply L-Hospital rule. 

As then .

.

.

Solution:

.