If the function $f(x) = \frac{1-\sin 2x + \cos 2x}{1+\sin 2x + \cos 2x}$ for $x \neq \frac{\pi}{2}$ and $f(x) = k$ for $x = \frac{\pi}{2}$ is continuous at $x = \frac{\pi}{2}$,then $k = $

If function $f$ is continuous at point $x = \pi$ and $f(x) = \begin{cases} kx+1; & x \leq \pi \\ \cos x; & x > \pi \end{cases}$ then the value of $k$ is $\dots \dots \dots$

If the function $f(x) = \left[ \frac{(x - 2)^3}{a} \right] \sin(x - 2) + a \cos(x - 2)$ is continuous in $[4, 6]$,then the value of $a$ is (where $[.]$ denotes the greatest integer function).

If the function $f(x)$,defined below,is continuous in the interval $[0, \pi]$,then find the values of $a$ and $b$.
$f(x) = \begin{cases} x + a\sqrt{2}(\sin x), & 0 \le x < \frac{\pi}{4} \\ 2x(\cot x) + b, & \frac{\pi}{4} \le x \le \frac{\pi}{2} \\ a(\cos 2x) - b(\sin x), & \frac{\pi}{2} < x \le \pi \end{cases}$

If $f(x) = \left[\tan \left(\frac{\pi}{4} + x\right)\right]^{\frac{1}{x}}$ for $x \neq 0$ and $f(x) = k$ for $x = 0$ is continuous at $x = 0$,then $k = \dots$

Consider $f(x) = [x]|x^3 - 2x^2 - x + 2|$ in $[-\frac{3}{2}, \frac{9}{2}]$. The number of points where $f(x)$ is discontinuous is (where $[.]$ denotes the greatest integer function).