Related InterviewSolutions

• In a sphere the rate of change of surface area isA.8π times the rate of change of diameterB.2π times the rate of change of diameterC.2π times the rate of change of radiusD.8π times the rate of change of radius
• Find the rate of change of the volume of a sphere with respect to its diameter.
• If x = 2 cos t – cos 2t, y = 2 sin t – sin 2t, find\(\frac{d^2y}{dx^2}\)at t =\(\frac{\pi}{2}\).
• Find \(\frac{d^2y}{dx^2}\), where y = log \((\frac{x^2}{e^2})\).
• If y = 3 e2x + 2 e3x, prove that \(\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y\) = 0.
• If x = cos t + log tan \(\frac{t}{2}\), y = sin t, then find the value of \(\frac{d^2y}{dt^2}and\frac{d^2y}{dx^2}\).at t =\(\frac{\pi}{4}\).
• If x = 3 cot t – 2 cos3 t, y = 3 sin t – 2 sin3 t, find\(\frac{d^2y}{dx^2}\)