Rajasthan Technical University 2011-1st Sem B.Tech (Main/Back) ,- , Engineering Mathematics-I (Commto all Branches) - Question Paper
(b) If the side and angles of a plane triangle ABC vary in such a way that its circumradius remains constant, then prove that :
5a 5 b 8c
cos A cos B cos C
where, Sa,5fc and Sc are small increments in sides a, b and c respectively.
4 (a) Find the maximum value of u, where u = sin x sin,y sin(x + y)
(b) Find the Maxima and minima of u = x~ + y2 + z2 subject to
the conditions ax2 +by2 +cz2 - 1 and lx + my+nz = 0. Interpret the result geometrically.
8
UNIT - III
(a) Find the length of the arc of the parabola x2 = 4ay from the vertex to an extremity of the latus rectum.
(b) Find the surface area of the solid generated by the revolution of the astroid x2/3 + y2/3 = a2/3 about the x-axis.
(a) Evaluate the following integral by changing to polar coordinates :
6
1 _
0 x
8
(b) Show that :
o
B(m,n) = ambri J
(ax + b)m+n Km + n)
r v c i 2 *
m-1
m I n
x
8
*
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Attachment: |
| Earning: Approval pending. |
