If the function $f(x) = \begin{cases} \frac{(e^{kx} - 1) \tan kx}{4x^2}, & x \neq 0 \\ 16, & x = 0 \end{cases}$ is continuous at $x = 0$,then $k = . . . . . .$.

The function $f(x) = [x]$,where $[x]$ denotes the greatest integer function,is continuous at:

For what value of $k$ is the function $f(x) = \begin{cases} \frac{\text{log}(1+2x) \sin x^{\circ}}{x^2}, & x \neq 0 \\ k, & x = 0 \end{cases}$ continuous at $x = 0$?

Define $f: R \rightarrow R$ by $f(x) = [x] + \sqrt{x - [x]}$ for $x \in R$,where $[x]$ denotes the greatest integer function. Then the set of points at which $f$ is continuous is

Let $f(x) = \begin{cases} \frac{ax^{2}+2ax+3}{4x^{2}+4x-3}, & x \neq -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases}$ be continuous at $x=-\frac{3}{2}$. If $f(f(x)) = \frac{7}{5}$, then $x$ is equal to:

Which of the following functions is not continuous at $x = 0$?