The limit expression is.

(a)

LHospitals Rule: If  or  then .

Again apply LHospitals Rule :

Applying LHospitals Rule twice results in the original limit, so LHospitals Rule fails.

(b)

The limit expression is.

.

(c)

Graph the function .

Observe the graph :

As  tends to , the function value approaches to .

.

(a) Applying LHospitals Rule twice results in the original limit, so LHospitals Rule fails.

(b) .

(c)

Graph of the function .

As  tends to , the function value approaches to .