The number of discontinuities of the greatest integer function $f(x) = [x]$ for $x \in \left(-\frac{7}{2}, 100\right)$ is:

Let $k$ be a non-zero real number. If $f(x) = \begin{cases} \frac{(e^x - 1)^2}{\sin (x/k) \log (1 + x/4)}, & x \neq 0 \\ 12, & x = 0 \end{cases}$ is a continuous function,then the value of $k$ is

Let $f : [-1,3] \to R$ be defined as $f(x) = \begin{cases} |x| + [x], & -1 \leq x < 1 \\ x + |x|, & 1 \leq x < 2 \\ x + |x|, & 2 \leq x \leq 3 \end{cases}$ where $[t]$ denotes the greatest integer less than or equal to $t$. Then,$f$ is discontinuous at:

$f(x) = \begin{cases} 3x - 8 & \text{if } x \leq 5 \\ 2k & \text{if } x > 5 \end{cases}$ is continuous,find $k$.

If the function $f(x) = \frac{\log(1 + ax) - \log(1 - bx)}{x}$,$x \neq 0$ is continuous at $x = 0$,then $f(0) = $ . . . . . .

If $f(x) = \frac{1 - \sin x}{\log(1 + \pi^2 - 4\pi x + 4x^2)}$ is continuous at $x = \frac{\pi}{2}$,then $f\left(\frac{\pi}{2}\right) = $