Page 15 - Engineering Mathematics Workbook_Final

Calculus

(c) f is discontinuous only at one point
(0,1)
1 1
(c) (d) (d) f is continuous only at one point
45 10
(0, 1)
[JAM 2012]
[JAM 2013]

16. The value of the integral
2  2
  1 1 y 1 x dx dy = 3 _______ 19. The value of    x   dx dies between
+
0 y 0
______

−
2 2 1
(a) 2 2 (b) (a) 1 and 1.5 (b) 1.5 and 2
2
(c) 2 and 2.5 (d) 2.5 and 3
−
−
2 2 1 2 2 1
(c) (d) [IISC 2010]
8 9
2
2
20. The value of   x + y dx dy ,
[IISC 2009] D
2
2
2
,
17. Let [x] denote the greatest integer D = ( { , x y  ) R x  x + y  2 } x
function of x. The value of  for which is _______
the function
  2 7
 sin − x   , x  0 (a) 0 (b) 9




f ( ) x =      − x 2   is
 14 28
 ,  x = 0 (c) (d)

continuous at x = 0 is _____ 9 9
[JAM 2013]
(a) 0 (b) sin ( ) 1−
)
21. The area of the region ( { , x y ,
(c) sin 1 (d) 1
3
0 x y  , 1,  +  3 } is _____

x
y
[JAM 2013] 4 2
18. Let the function f(x) is defined by 9 7
 e x , x is rational (a) (b)

f ( ) x =  16 16
 e 1 x , x is irrational
−

for x  ( ) . Then ______ (c) 13 (d) 19
0,1
32 32
(a) f is continuous at every point in (0,1) [MS 2005]

(b) f is discontinuous at every point in
(0,1)

13