Find the value of \( \frac{\tan 60^\circ - \tan 30^\circ}{\tan 60^\circ + \tan 30^\circ} \)

Find the value of x for which the function f(x) = 2x3 - x2 - 4x + 4 has a maximum value

Integrate \( \frac{x^2-\sqrt{x}}{x} \) with respect to x

Determine the value of \( \int_{0}^{\frac{\pi}{2}} (-2 \cos x)\,dx \)

A man 40m from the foot of a tower observes the angle of elevation of the tower to be 30o, Determine the height of the tower

If \(y = (1 + x)^2\), find \(\frac{dy}{dx}\)

The volume of a hemispherical bowl is \(718\frac{2}{3}\,\text{cm}^3\). Find its radius.

If y = x cosx, find \( \frac{dy}{dx} \).

Find the size of each exterior angle of a regular octagon.