Page 23 - Engineering Mathematics Workbook_Final

Calculus

local minima at x = 4 and point of   4 x 2 / y x dy dx =
inflection at x = 1 are 79. e _______
0 0
(a) a = − 3, b = − 24 3 4
8
7
(a) 4e − (b) 3e −
(b) a = − 3, b = 24
4
9
4
(c) 3e + 7 (d) 3e −
(c) a = 3, b = − 24
80. The value of   xy dx dy where ‘R’
(d) a = 3, b = 24 R
is the region bounded by x – axis,
2
75. The function ordinate x = 2a and the curve x = 4ay ,
)
2
f ( ,x y = x − 3x + 4y − 10 at (2, is
3
2
0) has
a 3 a 4
(a) (b)
(a) a maximum (b) a minimum 4 3
(c) a saddle point (d) both (a) & (b) a 4 a 4
(c) (d)
76. The function 6 8
)
x
2
f ( , x y = x y − 3xy + 2y + has − y
81. The value of     e dy dx is
(a) No local extremum 0 x y

(b) One local minimum but no local 1 (b) − 1
maximum (a) 2 2

−
(c) One local maximum but no local (c) 1 (d) 1
minimum
82. By changing the order of integration, the
(d) One local minimum and one local 4 2 ax )
a
maximum double integral   f ( , x y dy dx
0 x 2
4a
77. The distance between origin and a point can be expressed as
+
nearest to it on the surface z = 2 1 xy   q s f ( , x y dx dy then q r =
)
is p r

2
(a) 3 (b) 2 (a) y (b) y

(c) 1 (d) None (c) 0 (d) y

78.  2  3 xy dx dy = _____ 1 1 x 2 1 x − − 2 y 2 dz dy dx
−
y= 0 x= 0 83.    = ____
−
2
2
0 0 0 1 x − y − z 2
(a) 9 (b) 18
(c) 27 (d) 6

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