The function $f(x) = \sin |x|$ is

If $f(x) = \begin{cases} \frac{\cos(ax) - \cos(bx)}{x^2}, & x \neq 0 \\ \frac{1}{2}(b^2 - a^2), & x = 0 \end{cases}$ where $a$ and $b$ are real and distinct constants,then:

The value of $p$ for which the function $f(x) = \begin{cases} \frac{(4^x - 1)^3}{\sin(\frac{x}{p}) \log(1 + \frac{x^2}{3})}, & x \ne 0 \\ 12(\log 4)^3, & x = 0 \end{cases}$ is continuous at $x = 0$ is:

If $f(x) = x\sqrt{1 - [x]^2}$,then (where $[.]$ denotes the greatest integer function):

If the function $f(x) = \frac{\sin 3x + \alpha \sin x - \beta \cos 3x}{x^3}$,$x \in R$,is continuous at $x = 0$,then $f(0)$ is equal to:

If $f(x) = \frac{4^{x-\pi} + 4^{\pi-x} - 2}{(x-\pi)^2}$ for $x \neq \pi$ is continuous at $x = \pi$,then $f(\pi) = k$. Find the value of $k$.