Page 25 - Engineering Mathematics Workbook_Final

Calculus

 3   5  (c) a = 3, b = 2 (d) a = 2, b = 3
(c) log       (d) log      
 2   4  98. Which of the following function is
continuous at x = 3.
1
 ! n n 
93. Lt   n     

n→   n   2, x = 3

 
(a) ( ) x =  x − 1, x  3
f
(a) 0 (b) e 

 x + 3 , x  3
 
1  3
(c) 1 (d)
e  4, x = 3

f
(b) ( ) x = 
+
sin2x a sin x  −  8 x x  , 3
94. If Lt = b where ‘b’ is
n→ 0 x 3  x + 3, x  3

f
finite then a = ____, b = ________ (c) ( ) x = 
 x − 4, x  3

(a) -2, -1 (b) 2, 1
1
(d) ( ) x = f , x  3
(c) 2, -1 (d) -2, 1 x − 27
3
95. The values of a and b such that  x + 3x a , x  1
+
2

f
+
2
a sin x b log (cos x ) 1 99. If ( ) x =  is
Lt =  bx + 2, x  1

n→ 0 x 4 2
differentiable for ‘x’ then a, b =
(a) -1, -2 (b) 1, 2
(a) a = 3, b = 5 (b) a = 1, b = 2
(c) -1, 2 (d) 1, -2
(c) a = 1, b = 3 (d) a = 3, b = 1
x
96. If y = + x + x + ....... then 100. If 4x − 7 = 5, then the value of
y ( ) 2 = 2 x − − x is
(a) 4 or 1 (b) 4 only 1 1
(a) 2, (b) ,3
(c) 1 only (d) undefined 3 2

97. The values of a and b for which the 3 2
function (c) ,9 (d) ,9
3
2
 2x + 1 if x  1

 
f

2
f ( ) x =  ax + b if 1 x  is 101. If ( ) x = x − 1 + x − 2 is not
3

 5x + 2a if x  3 derivable at x =


continuous every where (a) x = 0 (b) x = 1, 2
(a) a = 2, b = 1 (b) a = 1, b = 2 (c) x = 3 (d) none

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