Calicut University 2007 B.Sc Computer Science SECOND YEAR -ANALYTIC GEOMETRY AND CLCULUS - Question Paper
C31392
C 31392 (Pages 2) Name.Jr]ASJMfiL..'.V.'i/i..............
Reg. No..................................
SECOND YEAR B.Sc. DEGREE EXAMINATION, MAY 2007
Part IIIMathematics (Subsidiary)
Paper IANALYTIC GEOMETRY AND CALCULUS (2001 admissions)
Time: Three Hours Maximum : 65 Marks
Unit I (Analytic Geometry)
* i?" . (Maximum Marks 20)
\ ' 1. Find the Cartesian and cylindrical co-ordinates of the point whose spherical co-ordinate is
n - ' (6 marks)
,,. |*0 2. What does the equation become when it is transferred to parallel axes through the point (a, b-c). The equation is 0c a)2 + (y fe)2 = c2. t>c3'JSrj
, 3. Fm3 the vertex, focus, axis of symmetry and directrix of the parabola y2 + 2y + 4x - if = 0. J
. * (6 marks)
4. Find the Co-ordinates of the centre, foci and equation to the directions of the ellipse :
f- a** + 4y-12.-*+4 = o.,-4}, <+ -4)
(6 marks)
/s*j
7. po 5' Find the equation of the sphere described on the line joining (3, 4, 5) and (1, 2, 3) as diameter.
3 'b - 4'*- = O (3 marks)
6. Discuss and sketch the surface x2 +y2 = 4z. Lfopkc.
. 1 (3 marks)
Unit II (Differential Calculus)
(Maximum Marks 30)
A*1" . j
0' 7- Given the value of the hyperbolic function sinhx = - -, find the value of other five hyperbolic
3
functions. - i/To = 1 cci-Kxr Sin < v ~
x t rrr ' v ' '
irfc
(5 marks)
'' 8. Find where y = cos h (4 - 3x). 3 A ' (3 marks)
Turn over
2 C 31392
9- Find where y = secA"1 (sin 2*). *~2- (Urt**- S--*- ccr5P,v. 7o (3 marks)
A otrS **- Y '
fy iO. Find the tt11* derivative of fa _ 2, + CjJ. [jpp** +
(5 marks)
A*' . b N/v - 3<'0p'_
"11. Using Leibnitzs theorem find the nth derivative ofx3 log (1 + x). -0 (r~M( j " C* (6 xjarks) r \r -3 ,1'" -f- 3 * C*7~r
v<\12. Verify Rolls theorem for /U) = * (x - 1) on the interval (0, 1). (e. marks)
13. Find the points of inflextion of the curve y = x3 - 9x2 + 7x - 6. (6 marks)
<92U (92U jy
14. Verify that for = sin -1 -- (6 marks)
15. Verify Eulers theorem when u - x3 + y3 + 3x2z. (5 marks)
Unit DI (Integral Calculus)
(Maximum Marks 15)
1
,\ 16. Use the trapezoidal rule to evaluate the integral ofyOc) from 0 to from the table below :
2t
x 2it 3it 4 it 5tt 6it , , /L q 'li
XI 0 <2 I b *r I
12 12 12 12 12 12
y(x) : -00000 -25882 -50000 -70711 -86603 -96593 1.0000
(5 marks)
2 2 x y
17. Find the area of an elliptic quadrant of + s; 1- (5 marks)
a b*
qH8. Find the volume of the solid formed by the revolution about the major axis of nn ellipse with axes 2a and 36.
(5 marks)
19. Find the surface area of a sphere of radius a. (5 marks)
2 3
.20. Evaluate j / (y2 - 3a*) <y dx. (5 marks)
** 1 -3
Attachment: |
Earning: Approval pending. |