The radius of a spherical soap bubble is increasing at the rate of 0.3 cms -1. When r = 8 cm, the rate of change of its volume is
76. 8π cm3/sec
24.8 π cm3/sec
768 π cm3/sec
12 π cm3/ sec
The equation of the tangent to the curve x = a cos3 t,y = a sin3 t at t is:
x sec t - y cosec t = a
x sec t + y cosec t = a
x cosec t + y sec t = a
None of these
The radius of a circle is increasing at the rate of 0.1 cm/sec. When r = 5 cm, the rate of change of area is
π cm2/sec
0.1 cm/sec
5 π cm2/sec
2π cm2/sec
The length x of a rectangle is decreasing at the rate of 3cm/min and width y is increasing at the rate of 2cm / min.When x = 10 cm and y = 6 cm,find the rate of change of the area of the rectangle is
-2
2
4
-4
The equation of the normal to the curve y = sin x at (π, 0 ) is :
x + y = π
x + y + π = 0
x - y = π
x - y + π = 0
If f (x ) = a ( x + sin x ) + a is increasing, then the value of a is
a >0
a < 0
a = -1
a = -2
The equation of the tangent to the curve y = 2 x2 - 3x - 1 at the point (1,-2) is
x - y - 3 = 0
x - y + 3 = 0
x + y - 3 = 0
x + y + 3 = 0
If the radius of a circle, increases from 5 to 5.1 cm, find the increase in area
π cm2
π/2 cm2
2π cm2
π3cm2
The tangent to the curve y = e2x at the point ( 0,1 ) meets the x axis at
(0,a )
(2, 0 )
( -1/2, 0 )
f (x ) = √3 sin x + 3 cos x is max at x =
π/3
π/2
π/6
2π/3
