If $f(x) = \begin{cases} \dfrac{(8 - 2x)^{\frac{1}{3}} - 2}{3 - (243 + 5x)^{\frac{1}{5}}}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}$ is continuous at $x = 0$, then $k =$

If $y = x + e^x$, then $\dfrac{d^2 x}{dy^2}$ is equal to

Let $f(x) = x - 5$.
If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) =$ .....

The equation of the normal to the curve $xy + 7 = 0$ is $Ax + By + C = 0$, then