If the function $f(x)=\begin{cases} \frac{1-\cos x}{x^{2}}, & \text{for } x \neq 0 \\ k, & \text{for } x=0 \end{cases}$ is continuous at $x=0$,then the value of $k$ is

Let $f: R \to R$ be a function defined as:
$f(x) = \begin{cases} 5, & x \le 1 \\ a + bx, & 1 < x < 3 \\ b + 5x, & 3 \le x < 5 \\ 30, & x \ge 5 \end{cases}$
Then $f$ is:

Find all points of discontinuity of $f,$ where $f$ is defined by $f(x) = \begin{cases} x^3 - 3, & \text{if } x \le 2 \\ x^2 + 1, & \text{if } x > 2 \end{cases}$

At which points is the function $f(x) = \frac{x}{[x]}$,where $[.]$ denotes the greatest integer function,discontinuous?

If in the interval $[0,3]$,$f(x) = \begin{cases} x\{x\}^2, & x \notin I \\ x, & x \in I \end{cases}$,then which of the following statements is correct? (where $\{.\}$ denotes the fractional part function)

If $f(x) = \frac{1+\cos \pi x}{\pi(1-x)^2}$ for $x \neq 1$ is continuous at $x=1$,then $f(1)$ is equal to