Page 18 - Engineering Mathematics Workbook_Final

Calculus

[MS 2009] 38. Let the function  : 0, ) → R is given
f
2 −
3 − 2 x by ( ) x = x e . Then the maximum
x
x
f
34. Lt
x
x→ 0 4 − 3 x value of f is___
3 2 − 1 − 2
(a) (b) (a) e (b) 4e
4 3 − 3 − 4
3 ( ) (c) 9e (d) 16e
3
2
(c) loge (d) log
4 2 [MS 2011]
3
[IISC 2006] 39. Let D be the triangle bounded by y axis,
=
the line 2y  and the line y = x .
1
35. Lt (n + 5 4n 3 ) − 5 n equals ________ cos y
n→  Then the value of   dx dy =
D y
4
(a) 4 (b) _______
5
1 3
5 (a) (b)
(c) 0 (d) 2 2
4
(c) 1 (d) 2
[IISC 2006]
[MS 2011]
36. The value of
1    1 e − 1 2 ( x + 2 y 2 ) dx dy = ________ 40. The volume of the solid revolution

2 − − generated by revolving the area bounded
by the curve y = x and the straight
 1
(a) (b) lines x = 4, y = about the x-axis, is
0
4 2
___________
1 1
(c) (d) (a) 2 (b) 4
4 2

[MS 2010] (c) 8 (d) 12

+
37. The value of   e − x y dx dy , whose [MS 2012]
S 41. The value of∫ ∫ 2
1
2


S = ( { , x y ), 0   1, y  0,1 x +  2} 0 2
x
y
equals _____________
(a) e + 1 (b) 1
(a) 1 (b) 2
2
−
−
2
2
1
e
(c) e − e (d) e − (c) e − 1 (d) e
[IISC 2005]
[MS 2010]

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