The set of points of discontinuity of the function $f(x) = x - [x]$, where $x \in R$, is:

If the function $f(x)$ defined by $f(x) = \begin{cases} x \sin \frac{1}{x}, & x \neq 0 \\ k, & x = 0 \end{cases}$ is continuous at $x = 0$,then $k = . . . . . .$

If $f(x)$ is continuous on its domain $[-2,2]$,where $f(x) = \begin{cases} \frac{\sin ax}{x} + 3, & -2 \leq x < 0 \\ 2x + 7, & 0 \leq x \leq 1 \\ \sqrt{x^2+8} - b, & 1 < x \leq 2 \end{cases}$ then the value of $2a + 3b$ is

If $f(x) = \begin{cases} \frac{8^x - 4^x - 2^x + 1}{x^2} & , \text{if } x > 0 \\ e^x \sin x + kx + \lambda \log 4 & , \text{if } x \le 0 \end{cases}$ is continuous at $x = 0$,then the value of $500 e^\lambda$ is

Let $f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2}, & x < 0 \\ a, & x = 0 \\ \frac{\sqrt{x} + \sqrt{2}}{\sqrt{16 + \sqrt{x}}}, & x > 0 \end{cases}$
If $f(x)$ is continuous at $x = 0$,then the value of $a$ is

Examine the following function for continuity: $f(x) = \frac{x^{2} - 25}{x + 5}, x \neq -5$.