Andhra University 2007 B.E Computer Science MATHEMATICS - I - Question Paper

I Year B.E./B.Tech Degree exams
MATHEMATICS - I
(Common to All Branches)
Time : 3 hours Maximum : 75 Marks
ques. one is compulsory
ans any 4 from ques. two to 8
All ques. carry marks
5
b) find Taylor’s expansion of 1( Tan??( y/x) about (1,1) upto
and including the 2nd degree terms.
3. a) Evaluate
/
2 2
0 /
( )
a x a
x a
????x ??y dx dy by changing the order of
integration.
b) Determine the M.I. about the X-axis of the area of a triangle
with the vertices A(1,1), B(2,1) and C(3,3).
4. a) obtain the equations to the line that intersects the lines
x?y?z?1, 2x?y?z?2,x?y?z?3,
2x?4y?z?4and passes through the point (1,1,1)
b) obtain the formula of the sphere having its center on the plane
4x?5y?z?3and passing through the circle
x2?y2?z2?2x?3y?4z?8?0, x?2y?z?8
5. a) Show that if a series ??un is convergent than
n 0
n
Lt u
??
??.
b) Test the convergence of the subsequent series
2 one three two four 3
..........
1 two 3
???????????
6. a) Show that the harmonic series of order p,
1
1
np
??
converges for p > one and diverges for 0 < p < 1.
6
b) Test for uniform convergence of the subsequent series
sin two sin three sin 4
sin ............
2 two three 3 four 4
x x x
x?????????
7. Express ( ) f x ?|x|,???x???as a Fourier series. Hence
obtain
2
2 2
1 1
1 ................ .
8 three 5
???????????
8. find the half range sine and cosine series for the function
f(x)?(x?1)2,0?x?1.
7
1. a) State Culey Hamilton theorem
b) Product of the eigen values of
1 2
3 4
A
???
????
???
is ?
c) Solve 22 0
dy
x y
dx
???
d) obtain the complementary function of (D2?3d?4)Y?0
e) obtain the laplace transform of t Sin t.
2. a) obtain the rank of
5 six seven 8
6 seven eight 9
11 12 13 14
16 17 18 19
???
???
???
???
???
???
b) For what values of k the equations
x?y?z?1, 2x?y?4z?k, 4x?y?10z?k2 have a
solution and solve them completely in every case

Earning:   Approval pending.