Page 22 - Engineering Mathematics Workbook_Final

Calculus

(a)  (b) 2 dy
69. If x + y y = x c then at (1, 1) is
dx
(c) 0 (d) 1
−
(a) 1 (b) 1
x y
2
66. If  = 5 5 then (c) 0 (d) 2
x + y 2
2
x  + 2 xy  + y  = ____ 70. If u = x e z where y = a − 2 x ,
2
2
2
y
xx xy yy
du
2
1 1 z = sin x then find at (0, 1, 1) is
(a)  (b) −  dx
4 4 ______
3 3 −
(c)  (d) −  (a) e (b) e
4 4
−
1
(c) e (d) 2e
  1 4 1 4  
z
y
67. If z = sin − 1   x + y 1   then 71. If u = f (2x − 3 , 3y − 4 , 4z − 2x )
 1 6    then 6u + 4u =
6
 x − y  x y
x z + 2xy z + y z = ______ (a) 2u− z (b) 8u
2
2
xy
yy
xx
z
−
1 (c) 3u (d) 3u
2
(a) tan z (tan z − 11 ) z z
144
Maxima & Minima
1
(b) tan z 72. The maxima & minima of the function
12 x
2
f ( ) x =  (t − 3t + ) 2 dt occurs
tan z 0
2
(c) (sec z − 11 ) respectively at
144
(a) x = − 2 and x = 1
(d) None of these
68. If (b) x = − 1 and x = 2
u ( , x y = ) x 2 tan 1 ( / y x − ) y 2 tan − 1 ( / x y ), (c) x = 2 and x = 1

x  0, y  0then
(d) x = 1 and x = 2
(
+
x 2 ( 2 / u  x 2 ) 2xy  2 / u  x ) y + y 2 ( 2 / u  y 2 ) =
73. The maximum value of the function
f ( ) x = x − 9x + 24x + in [1, 6] is
5
2
3
−
(a) u (b) u ______
(c) 2u (d) 3u 74. The values of ‘a’ and ‘b’ for which the
function ( ) x = x + ax + bx has
3
f
2

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