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
The interval in which x2 + 2x - 5 is strictly increasing is
(1, 0 )
( 0,1 )
If f (x ) = a ( x + sin x ) + a is increasing, then the value of a is
a >0
a < 0
a = -1
a = -2
If y = 7x - x3 and x increases at the rate of 4 units per second, how fast is the slope of the curve changing when x = 3?
32
27
70
-72
The side of a cube is equal to the diameter of a sphere.If the side and radius increase at the same rate then the ratio of the increase of their surfaces is
The equation of the tangent to the curve y = be -x/a at the point where x = 0 is:
None of these
f ( x ) = 1 + 2 sin x + 2 cos 2 x, 0 ≤ x ≤ π/2 is maximum and minimum respectively at x =
π/6, π/2
π/2, π/6
π/3, π/3
π/3, π/2
The value of n for which the length of the subnormal of the curve xyn = a n + 1 is constant
1
-1
2
-2
The tangent of the curve x2 + y2 – 2x -3 = 0 is parallel to axis at the point:
(2, ± √3)
(1, ± 2)
( ± 1, 2 )
( ± 3, 0 )
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