Unit-2

Practice Theory Question

1. If , prove that ?
2. If  ,prove that  ?
3. Find the  nth derivatives of

4.     If ,prove  that 

5.     If  ,  prove  that

   . Hence  find 

6.     Evaluate the following  limits:

7.       Show the equation of the tangent at any point to the curve

Also show that the portion of the tangent intercepted between the axes is of constant length?

8.     Find the equation of the normal  at any point to the curve

9.     Prove that the pedal equation of the asteroid

10. Find the pedal equation of the curve ?

11. Find the radius of curvature at any point of the following curves:

1. Cycloid:
2. Curve  :

12. Find the maximum and minimum values of ?

13. Find the extreme value of the function ?

14. Find the asymptotes of

15. If , prove that

16. If , prove that .

17. If compute ?

18. Expand     in   power of   and     using Taylor’s theorem?

19. Expand in power of  x and y    as far  as  terms  of third degree?

20. Find the maxima and minima of ?

21. Find the maximum and minimum distances of the points from the   sphere