University of Mumbai 2008-2nd Sem B.E F.E maths II - Question Paper
First Year engineering semester two Mathemathics II 2008.
Please obtain the attachment.
20
N.B.(1) Question No. 1 is compulsory.
(2) Attempt any four questions from remaining six questions.
1. Prove that
,2
00 -x
[ x e 1(4 dx x f e-l=- dx = %= .
(b) Use the rule of D.U.I.S. to prove that
a > 0
-2 -Jn
given J e dx -
o
jpY' Solve
1 1 1 y + y3 + x2 dx + ( x + xy2 ) dy = 0 .
3 2 J 4
j Use Taylors series method to find y at x = 0-2 given n. _o7)v? Ax.
dy 2 ' e
=1 + y with y = 0 at x = 0.
dx
Solve ? 6
/' " (p? + D2 + D + 1) y = sin2 x
1 molve V 7
Q i (D2 + 2) y = ex cos x + x2 e3x
where R is a triangle whose vertices are (0, 0), (1,1) and (0, 1).
Find the mass of Lamina in the form of cardioide r = a (1 + cos 0) if the density at any 6 point varies as its distance from the pole of cardioide.
a x + 3a
aChange the order of Integration J J f (x-y) dx dy. 7
X 0
ytf'Solve using Runge-Kutta method of order 4. 7
dy y
= - xn = 1, yn=1, for x = 1-2 with h = 0-1. dx x 0 0
that * - 6
[-*+ 1
J (1+x)7 _ 960 *
[b/So\v& = x + 3y, x0 = 0 by Eulars modified method for x = 0-1 in one step. j
X * y = 1
Compare the answer with exact value.
(p) Solve : 7
(1 + x)2 $ + (1+x) f + y = 4 005 <l09 (1+x)) I turn over
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Attachment: |
| Earning: Approval pending. |
