PART 8

Answer any 2 complete questions each having 7 marks

11. A ball is dropped from a height of h feet and on each bounce rises 75% of the
distance it has fallen previously. If it travels a distance of 21 feet what is h?

12.Use Ratio Test for absolute convergence to find whether 076 series

2 (- 1)k+1 2k
2 प्रा converges.
k=1 ∎

13.Find the Maclaurin’s Series for =

Answer any 2 complete questions each having 7 marks

14.For the surface 4x” + 972-182 = 2
a. Find the equation of the elliptical trace in the plane
0. 271/3
c. Find the length of the major and minor axes of the ellipse.

lim (x*+y? 11102 + 2
15. ष्व ಉಗ +) प +)

2. 472
16. Let f(x, ४) = व्व Determine the limit of f (x, y) as

(x, y) approaches (0, 0) along the curve C. where C is
(a)x=0 ൫50 (©) y=x
(d)y=x* (e)x= y?

Answer any 2 complete questions each having 7 marks
∙ dw ⋅
17.Use chain rule to find ಸ್‌ 1/4 if
Is

1 = 2 - 71916; r=Vs: 0-74
18.Locate all relative extrema and saddle points of f(x, y)=x?txy-2y-3x+]

19. The volume ۷ of a right circular cone of radius r and height h is given by =

‎Suppose that the height decreases from 20 to 19.95 units and the radius‏ سی