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

Discuss the continuity of the function $f$ defined by
$f(x) = \begin{cases} x + 2, & \text{if } x \le 1 \\ x - 2, & \text{if } x > 1 \end{cases}$

Let $[t]$ represent the greatest integer not exceeding $t$ and $C=1-2e^2$. If the function $f(x)=\begin{cases} [e^x], & x < 0 \\ ae^x+[x-2], & 0 \leq x < 2 \\ [e^{-x}]-C, & x \geq 2 \end{cases}$ is continuous at $x=2$,then $f(x)$ is discontinuous at

The points at which the function $f(x) = \frac{x + 1}{x^2 + x - 12}$ is discontinuous,are

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{2 \sin x-\sin 2 x}{2 x \cos x}, & \text{if } x \neq 0 \\ a, & \text{if } x=0 \end{cases}$, then the value of $a$ so that $f$ is continuous at $x=0$ is