A B1A216S (2015 Admission) Pages:2

(Answer any 2 questions. Each question carries 7 marks)
14) Find the equation of the paraboloid z = + 12 in the cylindrical and spherical

coordinates.

15) Find F(f(x).g(y)h(z) if ‏درج ر)گط‎ 1 ८ Seger? ട്‌, h(z)= 227

16) By converting into polar coordinate evaluate 7, പ്‌ “+ 7 In | (x 74 y? 1 )
(കോര)

(Answer any 2 questions. Each question carries 7 marks)
17) Find the local linear approximation L ‏نر ركه‎ 2) = xyz at the point P(1,2,3). Compare the
error in approximating f by L at the point Q(1 001, 0000, 3.003) with the distance PQ.
18) Find the relative extrema of f(x, 1) = 96 23) + ‏شر‎ —Ry

19) If fis a differentiable function of three variables and suppose that

w= f(x—y,y—z,2—x) Show that ‏یچ‎ ಲ್‌

(Answer any 2 questions. Each question carries 7 marks)
20) Suppose that a particle moves along a curve in 3-space so that its position vector at time 1
15 r(t) = 4008 nti +4sin xij + 11. Find the distance travelled and the displacement of

the particle during the time interval 15/55