132487

3 D 12033
21. Find the length of the Cardioid r =1+cos0.
22. Find the parametric equations for the line of intersection of the planes defined by 3x—y+2z=1
and 2x+3y-z=4.
23. Find the velocity vector, acceleration vector and speed of a particle with position vector :
r(t) =e i+ tt? j+e**k,t 0.
(5 x 6 = 30 marks)
Section C
Answer any two questions.

Each question carries 10 marks.

24. (a) Find the derivative of see '(e™*).

“دأ :0 جه

sinx
(b) Evaluate ‏جا‎ (=) ~

25. (a) Find theareaS ofthe surface obtained by revolving the circle r =cos9 about the line 9 = 7/2.

(b) Show that the surface area of a sphere of radius ris 47,2.

n!

26. (a) Determine whether the series 27 is convergent or divergent.
n=

on

3 is convergent and find its limit.

(b) Show that sequence |

27. (a) Find an equation in rectangular co-ordinates for the surface with spherical equation 0 = 4९080 .
(b) A moving object has an initial position and an initial velocity given by the vectors
r(0)=2+2j+k and v(0)=2+2k. Its acceleration at time ¢ is a(t) = 6t i + j + 2k. Find its

velocity and position at time ¢.
(2 x 10 = 20 marks)

132487