Practice Exercises: Successive differentiation   (Continued)

4. Using induction on , show that

(i)  For

(ii) For

5. The radius of the circular disc is increasing with time (think of oil pouring from a tanker in sec). Find the rate of     change of the area of the disc to the radius of the disc. How fast is the area increasing when radius is 4km, if the     rate of change of the radius is 5 cm/sec.