Page 26 - Engineering Mathematics Workbook_Final

Calculus

102. A real function tan x tan x
  x + 2  , x for x  0 (a) (b)

f ( ) x =  2y − 1 2y − 1
  x +  x + 5sin , x x  0
2
3

2
f
. If ( ) x is twice differentiable then (c) sec x (d) sec x
2y − 1 2y − 1
(a)  1, =  = 0 (b)  1, =  = 5 dy
+
(c)  5, = = − 10 (d)  5, = = 5 106. If x y = a b (x + ) y a b then dx =

 2x  x 1
103. The derivative of sin − 1   2     with (a) (b)
+
 1 x  y y
 2x 
respect to tan − 1   2     is equal to 1 y
−
 1 x  (c) (d)
x x
(a) 0 (b) 1
107. By applying, Rolle’s theorem for
2x sin x

(c) (d) 2 f ( ) x = in 0, , the value of
−
1 x 2 e x
)
c  (0, is
104. If x = ( a  sin − ) ,

2
d y  
y ( a  = cos − ) then = (a) (b)
dx 2 6 4

1  
(a) −  (c) (d)
a sin 2 2 3
2
108. Which of the following function satisfied
1  all the conditions of Rolle’s Theorem in
(b) − cosec 4
4a 2 the interval [0,1]

1 f x = 
(c) − sec  2 / 2 cosec   4 / 2 (a) ( ) tan x
4a
 1
1  x , 0  x 

(d) sec  2 / 2 cosec   4 / 2  2
f
4a (b) ( ) x = 

 − , 1  x  1
1 x
 2

105. If y = tan x + tan x + tan x + .....
dy 109. By applying Lagranges mean value for
then = the function
dx

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