The value of f(0) so that the function $f(x) = \dfrac{(256 - 8x)^{\frac{1}{4}} - 4}{16 - 4(64 + 3x)^{\frac{1}{3}}}$, $x \neq 0$ is continuous at $x = 0$, is

The derivative of $\sin\left(\log\left(\dfrac{x+3}{x}\right)\right)$ is

If $e^y + xy = e$, then the ordered pair $\left(\dfrac{\text{d}y}{\text{d}x}, \dfrac{\text{d}^2 y}{\text{d}x^2}\right)$ at $x = 0$ is equal to

The surface area of a spherical ball is increasing at the rate of $4\pi\ \text{cm}^2$/second. The rate at which the radius is increasing when the surface area is $16\pi\ \text{cm}^2$ is