The length, breadth and height of a cuboid depend on time as `L=sin t` , `B=t^(2)` , `C=t` The rate of change of volume with time at `t=(pi)/(2)` is `(k pi^(2))/(4)`. Value of `k` is

If radius of a spherical bubble starts to increase with time t as r=0.5t . What is the rate of change of volume of the bubble with time t=4s ?

The position of a particle moving on a straight line depends on time t as x=(t+3)sin (2t)

The vector vec A varies with time as vec A=that i-sin pi that j+t^(2)hat k. Find the derivative of the vector at t=1

The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is 2x^2 times its breadth and the height is 3/2x y\ times of length. Find the volume of the cuboid if its breadth is 6y^2

If x=a(cos t+t sin t) and y=a(sin t-t cos t), then find the value of (d^(2)y)/(dx^(2)) at t=(pi)/(4)

If x=a(cos t+t sin t) and y=a(sin t-t cos t), then find the value of (d^(2)y)/(dx^(2)) at t=(pi)/(4)

The length of the subtangent to the ellipse x=a cos t, y= b sin t at t = pi//4 is

If x=sin tcos 2t,y= cos tsin 2t ,then " at " t= (pi)/(4) ,(dy)/(dx)

If x=sin t-t cos t and y = t sin t +cos t, then what is (dy)/(dx) at point t=(pi)/(2)?