Calicut University 2007 B.Sc Computer Science FIRST YEAR ,IL- - Question Paper
C
C 30817 (Pages 2)
Name. . .;U.VJ.................
Reg. No..................................
FIRST YEAR B.Sc. DEGREE EXAMINATION, MARCH/APRIL 2007
Part IIISubsidiary Mathematics Paper IANALYTIC GEOMETRY AND CALCULUS
(2001 Admissions)
Time : Three Hours - Maximum : 65 Marks
Maximum marks from Unit I is 20,
Unit II is 30 and Unit III is 15.
Unit I (Analytic Geometry)
(Maximum Marks 20)
KFind the cylindrical and spherical co-ordinates of the point whose Cartesian co-ordinates are (0, 0, 1).
(6 marks)
S: Find the new equation of the line x - 3$,+ 6 = 0 when
' y 3- Find the equation of the parabola with focus (-% - 1 Hand vertex ( T, - X) (6 marks)(
4>. Find the eccentricity, latus rectum, foci and directrices of the ellipse %2 + 25y2 ~ 225, (6 marks) 5. Find the equation of the sphere with centre at (1, -2, 3) and radius = 5 units. (3 marks)
(X; Discuss the sketch the surface xz + 9z2 = 9.
Unit II (Differential Calculus)
(Maximum Marks 30)
29
Y._ Given the value cosh x = find the values of other five hyperbolic functions. (5 marks)
dy '/V
8. .-Find where y = sech (3 marks)
in is changed to the point (3, 2). |
\
(6 marks) Tr "/
(3 marks)
&
/ . dy y9. Find ", wherey = sinh1 (tan x).
ylO. Find the n.th derivative of
(3 marks)
o
(5 marks)
Turn over
W - Uh V "i~ lin| + 2 V*Wj (i _j - T ,v*v ,/a
Using Leibnitzs theorem; find the /Ith derivative of x2 sin Zx. Verify Rolls theorem for fix) - (.t + 2)2 {x - 3) in the interval {-2, 3J.
u i* 4.
Find the points of inflexion of the curve y = x4 - 6x2 + 8bc ~ 1.
C 30817
(6 marks) (6 marks) (6 marks)
(6 marks) (5 marks)
at. 2. ' 13.
2..
ifiu <?2u ,____
Verify that for u = sin (x + y) + log (x + y).
14.
15.
Verify Eulers theorem when u = x* ~ 4x3y + 3 xS - y*.
Unit III (Integral Ualculus) (Maximum 15)
<V V-
U
-\r>ply Simpsons rule to evaluate J to two places of decimals by dividing tin;
four equal parts.
Find the area of the loop of the curve y2 = x4 (x + 2).
Find the length of the curve 27 y2 = 4s3 from x 0 to x 3.
Find the volume generated when the part of the curve y = <? sin x between x ~ 0 and .t about the .t-axis.
UV' rt
range into
(5 marks)
18.
(5 ixiarAii)
(5 marks) < jc revolves
(5 marks) (5 marks)
M2*2) r
0. Evaluate J J xy dx dy,
\A'
aV A A(/i
Vi- "0 /
p-
&
V-
\
+ri '
Attachment: |
Earning: Approval pending. |