The length x of a rectangle is decreasing at the rate of 5cmm and the width y is increasing at the rate of 4cmm When x=8cm and y=6cm, find the rate of change of (a) the perimeter and (b) the area of the rectangle.
If the function y=f(x) is represented as x=ϕ(t)=t5−5t3−20t+7, y=ψ(t)=4t3−3t2−18t+3(∣t∣<2), then find the maximum and minimum values of y=f(x)˙
The tangent at any point on the curve x=acos3θ,y=asin3θ meets the axes in PandQ . Prove that the locus of the midpoint of PQ is a circle.
An electric light is placed directly over the centre of a circular plot of lawn 100 m in diameter. Assuming that the intensity of light varies directly as the sine of the angle at which it strikes an illuminated surface and inversely as the square of its distance from its surface, how should the light be hung in order that the intensity may be as great as possible at the circumference of the plot?
Find the maximum value and the minimum value and the minimum value of 3x4−8x3+12x2−48x+25 on the interval [0,3]˙
A curve is given by the equations x=sec2θ,y=cotθ˙ If the tangent at Pwhereθ=4π meets the curve again at Q,then[PQ] is, where [.] represents the greatest integer function, _________.