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Course: B.Tech.
Subject: Engineering Mathematics-I
Code: TMA-101
1. If
u xyz,v xy yz zx,w x y z= = + + = + +
.
The prove that:
( )
( ) ( )( )( )
u,v,w x y y z z x
x, y,z
= − − −
.
2. If
2 3 1 3 21
1 2 3
1 2 3
x x x x xx
y ,y , y
xxx
= = =
.
The prove that:
( )
( )
1 2 3
1 2 3
4
y ,y ,y
x ,x ,x
=
.
3. If
2 2 2
u xy yz zx,v x y z ,w x y z,= + + = + + = + +
determine whether there is a functional relationship
between u, v and w and if so, find it.
4. If
3 3 2 2 3 3
u v x y,v u x y+ = + + = +
The prove that:
( )
( )
( )
( )
22
2
yx
u,v
x, y uv u v
−
=
−
.
5. If u, v and w are the roots of the equation
( ) ( ) ( )
3 3 3 0x y z
− + − + − =
, in
then find
( )
( )
,,
,,
u v w
x y z
.
6. If
1 1 2 3 4 1 2 2 3 4 1 2 3 3 4 1 2 3 4 4
u x x x x ,u u x x x ,u u u x x ,u u u u x ,= + + + = + + = + =
Then prove that:
( )
( )
1 2 3 4 32
1 2 3
1 2 3 4
x ,x ,x ,x u u u
u ,u ,u ,u
=
.
7. Find the extreme values of function the functions:
(i)
( )
2 2 3
, 4 3u x y y xy x x= + + +
(ii)
33
3.u x y axy= + −
(iii)
( )
311
,f x y xy a xy
= + +
(iv)
( )
2 2 2 2
, 5 8 5u x y x y x xy y= − − −
(v)
( )
, sin sin sin( ).u x y x y x y=+
ASSIGNMENT SHEET-03