Calicut University 2007 B.Sc Computer Science SECOND YEAR , EMBER- - exam paper
D41141
41I4I (Pages: 2)
Name.}!EL5Ml.:.\i;.kl........... Reg. No.................................SECOND YEAR B.Sc. DEGREE EXAMINATION, DECEMBER 2007
Part IIIMathematics Subsidiary Paper IANALYTIC GEOMETRY AND CALCULUS (2001 admissions)
Time : Three Hours Maximum : 65 Marks
Maximum, marks from Unit / is 20, Unit 11 is 30 and Unit HI is 16.
Unit I (Analytic Geometry and Calculus)
(Maximum marks: 20)
41I4I (Pages: 2)
Name.}!EL5Ml.:.\i;.kl........... Reg. No.................................1. Find the cylindrical and spherical co-ordinates of the point whose Cartesean co-ordinates are
41I4I (Pages: 2)
Name.}!EL5Ml.:.\i;.kl........... Reg. No.................................41I4I (Pages: 2)
Name.}!EL5Ml.:.\i;.kl........... Reg. No.................................(6 marks)
2. Transform the equation x2 - 6x + 2y2 + 7 = 0 to new rectangular axes through the point (3, 1)
parallel to the x and y axes. What are the new co-ordinates of (2,4) ?
'.v(6 marks) (6 maiarS;
3. Find the equation of thejiarahola with focus <4,3) and vertex(4, 1). c;.*<
4. Find the eccentricity, latus rectum, foci and directrices of the ellipse 7jc2 + 16y2 = 448.
(6 marks) (3 mfcpks)
5. Find the equation of the sphere with centre at (2,-3, 4) and radius 5 units.
\ ;
6. Discuss and sketch the graph of the cylinder represented by the equation y2 + 422 = 16.
(3 marks)
(5 mWks) (3 msbJcs)
Unit II (Differential Calculus)
(Maximum marks : 30)
13
7. Given the value cot h x = , Find the values of all other hypenbolic functions.
dy f xz
Find where y = seek + 1 dx 2-
dy (X
(3 maiks)
10. Find the derivative of
(5 marks)
(6 marks) Turn over
(x-1)2 Gc -2)'
2 B 41141
12. Verify Rolls theorem for the function f {x) = 8x3 -14x2 + Ix -1 in the interval
13. Find the points of inflexion of the curve x = y log
(I 1 4 * 2 J *
(6 marks) (6 marks)
(6 marks) (5 marks)
-\2
O U O IK rt i V o v
14. Verify that ITST fr tan-1-y2tan_1 .
wccy oyox % y
* t
15. Verify Eulers theorem when u = ctxe + bxy+try5 + ky6,
Unit III (Integral Calculus)
(Maximum marks : 15)
dx
16. Obtain an approximate value of log- , using Simpsons rule, f-- after dividing the range into
o1+*
eight equal parts.
.(5 marks)
17. Find the area of the loop of the curve 4y2 = (x 5)2 (x 1). (5 marks)
18. ind the length of the arc of the semi-cubical parabola y2 - x3 from the origin to the point (4, 8).
(5 marks)
19. Show that the surface area of the solid generated by the revolution of the loop of the curve x = t2,
y = t - *3 about the x axis is 3n.
|
Attachment: |
| Earning: Approval pending. |
