Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is:
A cylindrical tank of radius 10 cm is being filled with sugar at the rate of 100π cm3/s. The rate at which the height of the sugar inside the tank is increasing is:
The sum of the payoffs to the players in the Nash equilibrium of the following simultaneous game is ............
Player Y | ||
---|---|---|
C | NC | |
Player X | X: 50, Y: 50 | X: 40, Y: 30 |
X: 30, Y: 40 | X: 20, Y: 20 |