List of top Statistical Science Questions on Calculus asked in ICAR AIEEA (PG)

The value of \(\lim_{x \to 0^+} \left(\frac{1}{x} - \frac{1}{\sin x}\right)\) is:

For the function \(f(x) = x^3 - 3x\) on \([-1, 3]\), the points of maxima and minima are respectively:

The value of \(\lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{\sin x}\) is:

The value of \(\lim_{x \to \infty} \sqrt{\frac{3x - 5}{x - 2}}\) is:

A particle moving on the x-axis has position \(x(t) = 2t^3 + 3t^2 - 36t + 40\) feet after an elapsed time of t seconds. Its velocity after 3 seconds is: