Page 37 - Engineering Mathematics Workbook_Final

Calculus

(b) a local minimum at x = 1 and a local 199. For the function
maximum at x = 2  y  1   x 
z = x tan − 1       + y sin −      + 2 ,
(c) local maxima at x = 1 and x = 2  x   y 

(d) local minima at x = 1 and x = 2 the value of x z  + y z  at (1, 1) is
 x  y
[JAM CA 2008]
 − − 1
2
196. If ( ) x = f  x ( t t − ) 1 dt , then (a) 4 sin 1
a

−
+
1
(a) f has a local maximum at x = 0 and a (b) + sin 1 2
local minimum at x = 1 4
(b) f has local minima at x = 0 and x = 1 (c)  + sin 1 2
−
−
1
4
(c) f has a local maximum at x = 1 and a
local minimum at x = 0  −
1
(d) + sin 1 [JAM CA 2005]
(d) f has local maxima at x = 1 and x = 0 4
=
=
2
3
x
f
197. If ( ) x = ax + bx + + 1 has a 200. For x r cos , y r sin , which of
local maximum value 3 at x = − 2, then the following is correct?
r    − 1
3 5 3 5 (a)  = sec and  = sin
(a) a = ,b = (b) a = ,b = x x r
4 2 2 4 r   
(b) = sec and = cosec
3 5 3 5  x  x
(c) a = ,b = (d) a = ,b =
4 4 2 2 r    1
(c) = cos and =
 x  x r cos
17
f x =
198. Let ( ) (x − 2 ) (x + ) 5 24 . Then r    − sin
(d) = cos and =
 x  x r
(a) f does not have a critical point at 2
[JAM CA 2005]
(b) f has a minimum at 2
 x 3

(c) f has a maximum at 2   , ( ,x y ) (0,0 )
)
201. If ( ,f x y =  x + y 2
2

(d) f has neither a minimum nor a  0 , otherwise
 
maximum at 2 then at (0,0)
[JAM MA 2006] f  f 
(a) and exist and are equal
 x  y

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