Cochin University of Science and Techology (CUST) 2008 B.Tech Civil Engineering Engineering Mathematics II - Question Paper
BTS (C) - I&n - 08 - 030 (A)
B. Tech Degree I & II Semester (Combined) Examination
IT/CS/EC/CE/ME/SE/EB/EI/EE 102 ENGINEERING MATHEMATICS II
(2000Scheme)
BTS (C) - I&n - 08 - 030 (A)
Maximum Marks: 100
Time: 3 Hours
(All questions carry EQUAL marks) Discuss the convergence of
(a)
1
(i)
(ii)
yjn + jn + l
l
, x x2 x3
1h---1--H--- + ...00
2 5 10
cosx cos2;c cos3x Prove that the following series converges absolutely 5I----1----I-... .oo.
(b)
(c)
I2 ' 22 ' 32
Find the first three non zero terms of the Taylor series expansion of ex sin Jt about x = 0.
(aT7 Oiscusshe convefgnowi- -
j x x ' ' - - : ' .
(i) 1--+----K...o
2 3 4
(ii) l + x + x2 + .....00
(b) Find the Taylor series expansion of cos x about Jt = 0.
(c) If y = sm~xx, showthat(l-x2)iy+2-(2+l)1-/22>/H=0.
(a) Solve the following system of equation by Gauss Elimination method:
III.
lx + 6y-5z = 30 3x-4 y + z =0 x+2y-3z = 10
(b) Using Cayley Hamilton theorem obtain the inverse of
|
2 |
3 |
4 |
|
3 |
4 |
-1 |
|
1 |
2 |
1 |
OR
8 -6 2
(a) Find the eigen values of A = 6 74
and find eigen vector corresponding
IV.
to the smallest eigen value.
Express the following matrix as the sum of a symmetric and a skew-symmetric matrix
4 2 -3 1 3 -6 -5 0 -7
V- (a)
(b)
