If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$ for $x \neq \pi$ is continuous at $x = \pi$,then the value of $f(\pi)$ is

If $f(x) = \begin{cases} e^x; & x \le 0 \\ |1 - x|; & x > 0 \end{cases}$,then

For the function $f(x) = \begin{cases} \frac{\sin^2(ax)}{x^2}, & x \neq 0 \\ 1, & x = 0 \end{cases}$,which one is a true statement?

If $f(x) = \begin{cases} x^2 - 1, & \text{if } x \ge 2 \\ x + 1, & \text{if } x < 2 \end{cases}$, then $\lim_{x \to 1} f(x) + \lim_{x \to 2} f(x) =$

If $f:(-7,7) \rightarrow R$ is defined by $f(x)=[x]$ for all $x \in (-7,7)$,then the number of discontinuities of $f$ is

Consider the piecewise defined function $f(x) = \begin{cases} \sqrt{-x} & \text{if } x < 0 \\ 0 & \text{if } 0 \leqslant x \leqslant 4 \\ x - 4 & \text{if } x > 4 \end{cases}$. Choose the answer which best describes the continuity of this function.