(a)

The limit expression is .

.

LHospitals Rule: If or then .

The limit is in the form of .

Therefore, the LHospital rule is applicable.

(b)

The limit expression is .

.

The limit is not in the indeterminate form.

Therefore, the LHospital rule is not applicable.

(c)

The limit expression is .

.

The limit is not in the indeterminate form.

Therefore, the LHospital rule is not applicable.

(d)

The limit expression is .

.

The limit is in the form of .

Therefore, the LHospital rule is applicable.

(e)

The limit expression is .

.

The limit is not in the indeterminate form.

Therefore, the LHospital rule is not applicable.

(f)

The limit expression is .

.

he limit is in the form of .

Therefore, the LHospital rule is applicable.

For (a), (d) and (f), LHospital rule is applicable.