ASSIGNMENT No. 1
(Units 1–9)
Q.1 a) Show that
11
ln ; 0dx ax b C ax b
ax b a
b) Find
35.
x
e Cos xdx
Q.2 a) Evaluate
2
22
23
( 1)( 2)( 3 5)
xx
x x x x
by partial fraction.
b) Find the area between
y Cosx
and
y Sinx
from
/4x
to
/4.x
Q.3 a) In a culture, bacteria increases at the rate proportional to the bacteria present. If the bacteria
are 200 initially and are tripled in 3 hours, find the bacteria present 6 hours later.
b) Find the general solution of the equation
2 3 2.
dy x y x
dx
Also find particular solution if y =
1 when x = 0.
Q.4 a) Suppose the axes of an xy-coordinate system are rotated through angle of
0
45
to obtain
an
xy
coordinate system. Find the equation of the curve xy = 1. Also identify and sketch
the curve.
b) Find the equation of tangent line to the curve
2
yx
at (2,4).
Q.5 a) Maximize the function f(x,y) = 4x+ 6y subject to constraints:
2 8, 2 14, 0, 0.x y x y x y
b) Find the equation of the circle passing through points A(10,15), B(11,14) and C(3,8).
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