The value of $f\left(0\right)$ so that the function $f\left(x\right)=\frac{2x-{\sin }^{-1}x}{2x+{\tan }^{-1}x}$ is continuous at each point in its domain is equal to

Let $f\left(x\right)=\left\{\begin{array}{ccc}\frac{1-\cos 4x}{x^2}& \text{ for }& x<0\\ a& \text{ for }& x=0\\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}& \text{ for }& x>0\end{array}\right.$

The value of $\left(a\right)$ for which $f\left(x\right)$ is continuous at $x=0$ is

Let $f\left(x\right)=\left\{\begin{array}{cc}\frac{\sin \pi x}{5x},& x\ne 0\\ k& ,x=0\end{array}\right.$

If $f\left(x\right)$ is continuous at $x=0$ then $k$ is