ASSIGNMENT No. 2
(Units 1–9) Total Marks: 100
Q.1 a) Determine whether following are even or odd functions.
i.
( ) tan cotf x x x
ii.
42
3
() 1
xx
fx x
iii.
3/ 4
( ) 10f x x
b) Let the real valued functions f and g be defined by
24
( ) 2 10, ( ) 4 5f x x g x x
. Find
i. fog(x) ii. gof (x) iii. fof (x)
Check whether fog (x) = gof (x).
Q.2 a) For real valued function f defined by,
2
2
21
( ) ; 1
1
x
f x x
x
, is
1()fx
possible. If yes than
find
1()fx
.
b) Find
0
2
lim 12
Sin Sin
Cos Cos
Q.3 a) Fin
2
0
1 2tan
lim 1 tan
b) Find the values of a and b so that the function
3
( ) 3
3
ax b if x
f x b if x
x b if x
is continuous at x=3
Q.4 a) Find
()fx
by first principal if
4/ 3
( ) .f x x
b) Find
5 5/ 3
(1 5 )
dy if y x x
dx
Q.5 a) If
2
1
2
tan(2tan ) .
x d y
y then find
a dx
b) A box with square base and open top is to have a volume V = xyz cubic dm. Find the
dimensions of the box which will require the least material
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