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Assignment - 1 Module-1 1.
Show that if it is possible to draw three normals from the point (a,0)to the parabola
2
y x
shown in the diagram, then a must be greater than ½. One of the normalsis the x-axis. For what values of a are the order other two normals perpendicular? 2.
Find the equation of the normal to the curve
y
x y x
where it cuts the x axis. 3.
Two cars start out 500 miles apart. Car A is to the west of car B and starts driving to the east at 35 mph and at the same time car B starts driving south at 50 mph. After 3 hours of driving at what rate is the distance between the cars changing. Is it increasing or decreasing? 4.
A boy starts walking north at a speed of 1.5 m/s, and a girl starts walking west at the same point P at the same time at a speed of 2 m/s. At what rate is the distance between the boy and the girl increasing 6 seconds later? 5.
1221111
432222
x x xdxdythat show x x x x yif
Module- 2 6.
Find the shortest distance from the point (1 + n, 0) to the curve
,0
n
yxn
7.
The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the shape of the largest beam that can be cut from a log of given size. 8.
Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides. 9.
Show that
53
()4712
fxxxx
assumes the value ‘9’ exactly once. 10.
When x is measured in degrees, what is the maximum slope possible for the curve y=sin(x) in the interval
[30,60]
.
Module- 3 11.
Find the area below
2
43
yxx
and above
32
7105
yxxx
over the interval
12
x
. 12.
Find the volume of a pyramid with a square base that is 20 meters tall and 20 meters on a side at the base. 13.
Find the volume of the object generated when the area between y = x
2
and y = x is rotated around the x-axis. 14.
Find the area of the region enclosed by the curves
f
(
x
) = cos
x
and
g
(
x
) = cos
x
- sin
x
over the interval [0,
]. 15.
Find the area of the region enclosed by the curves f(x) =
2
x
e
and g(x) =
2
x
e
and h(x)= 1/e. 16.
Evaluate i. ii.

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