A particle moves along the curve `y=x^(3/2)` in the first quadrant in such a way that its distance from the origin increases at the rate of `11` units per second. Then the value of `dx/dt` when `x=3` is given by

A particle moves along the parabola y=x^(2) in the first quadrant in such a way that its x-coordinate (measured in metres) increases at a rate of 10 m/sec. If the angle of inclination theta of the line joining the particle to the origin change, when x = 3 m, at the rate of k rad/sec., then the value of k is

A particle moves along the curve 12y=x^(3) . . Which coordinate changes at faster rate at x=10 ?

A particle moves along the curve x^(2)=2y . At what point, ordinate increases at the same rate as abscissa increases ?

If y=x^(3) and x increases at the rate of 3 units per sec; then the rate at which the slope increases when x=3 is.

A particle moves along the curve y=x^(2)+2x. At what point(s on the curve are the x and y coordinates of the particle changing at the same rate?

If y=7x-x^(3) and x increases at the rate of 4 units per second,how fast is the slope of the curve changing when x=2?

A particle moves along the curve y=(4)/(3)x^(3)+5 . Find the points on the curve at which the y - coordinate changes as fast as the x - coordinate.

Find the area bounded by the curve y=sqrtx,x=2y+3 in the first quadrant and X-axis.

Find the area bounded by the curve y=sqrtx,x=2y+3 in the first quadrant and X-axis.