(a)

Step 1:

The expression is .

Rewrite the expression as:.

Apply sum and difference rule .

.

Apply L-Hospital rule for

.

Apply formula .

.

Solution:

.

(b)

Step 1:

The expression is .

Rewrite the expression as .

Apply L-Hospital rule.

.

.

.

.

Solution:

.

(c)

Step 1:

The expression is .

Rewrite the expression as .

Apply L-Hospital rule:

.

Solution:

.

(d)

Step 1:

The expression is .

Apply quotient rule of logarithms:.

.

.

Solution:

.