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

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} a - \frac{\sin [x-1]}{x-1} & \text{if } x > 1 \\ 1 & \text{if } x = 1 \\ b - \left[ \frac{\sin [x-1] - [x-1]}{([x-1])^3} \right] & \text{if } x < 1 \end{cases}$ where $[t]$ denotes the greatest integer less than or equal to $t$. If $f$ is continuous at $x = 1$,then $a + b =$

Consider the piecewise defined function $f(x) = \begin{cases} \sqrt{-x} & \text{if } x < 0 \\ 0 & \text{if } 0 \leqslant x \leqslant 4 \\ x - 4 & \text{if } x > 4 \end{cases}$. Choose the answer which best describes the continuity of this function.

If $[x]$ denotes the greatest integer not exceeding $x$ and if the function $f$ defined by $f(x)= \begin{cases} \frac{a+2 \cos x}{x^2} & , x < 0 \\ b \tan \frac{\pi}{[x+4]} & , x \geq 0 \end{cases}$ is continuous at $x=0$, then the ordered pair $(a, b)$ is equal to

Examine the following function for continuity: $f(x) = \frac{1}{x-5}, x \neq 5$.

If $f(x) = \begin{cases} x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}$,then at $x = 0$ the function $f(x)$ is