Page 14 - Engineering Mathematics Workbook_Final

Calculus

8. Find the volume of the solid bounded ln ( x + y 2 )
2
above the surface z = − 2 y and 12. The value of   x + y 2 dx dy
1 x −
2
2
0
below by the plane z = .
where G = ( { , x y  ) R ,
2
[JAM 2006]

1 x + y  e 2 } is _____
2
2
9. Using change of variables evaluate
  xy dx dy where the region R is (a)  (b) 2
bounded by the curves xy = 1, xy = 3, (c) 3 (d) 4
y = 3x and y = 5x in the first
[JAM 2010]
quadrant. [JAM 2006]
n
10. Let A(t) denote the area bounded by the 13. The value of Lt  2 1 is
n→ 
=
curve y e − x , the x-axis and the k 1 = n + kn
straight lines x = − t and x t = . Then ________
)
Lt A ( ) t is _______ (a) 2 ( 2 1 (b) 2 2 1
−
−
t→ 
(a) 2 (b) 1 1
)
−
(c) 2 − 2 (d) ( 2 1
1 2
(c) (d) 0
2 [JAM 2015]

[JAM 2007] 14. Let V be the region bounded by the
planes x = 0, x = 2, y = 0, z = 0 and y + z
11. The function f defined by
 e 1/x x  0 = 1. Then the value of

f ( ) x =     y dx dy dz is __________
 0 x  0 v

1 4
(a) is differential for all real values of x (a) (b)
2 3
(b) is not differential at x = 0
1
(c) is not differential for x < 0 (c) 1 (d)
3
(d) is not differentiable for x > 0
[JAM 2011]
[IISC 2008] 1 z y

2 3
15. The value of    xy z dx dy dz
z= 0 y= 0 x= 0
is ___________

1 1
(a) (b)
90 50

12