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

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 $k =$

The function $f(x) = \frac{\log(1 + ax) - \log(1 - bx)}{x}$ is not defined at $x = 0$. The value which should be assigned to $f$ at $x = 0$ so that it is continuous at $x = 0$ is:

If the function $f(x) = \left(\frac{5x-8}{8-3x}\right)^{\frac{3}{2x-4}}$ for $x \neq 2$ and $f(2) = k$ is continuous at $x = 2$,then $k =$

If $f(x) = \begin{cases} (1+|\sin x|)^{\frac{a}{|\sin x|}}, & -\pi/6 < x < 0 \\ b, & x = 0 \\ e^{\frac{\tan 2x}{\tan 3x}}, & 0 < x < \pi/6 \end{cases}$ is continuous at $x = 0$,find the values of $a$ and $b$.

Given the function $f(x) = 2x \sqrt{x^3 - 1} + 5 \sqrt{x} \sqrt{1 - x^4} + 7x^2 \sqrt{x - 1} + 3x + 2$,then: