If $f(x) = \begin{cases} [x] + [-x], & x \ne 2 \\ \lambda, & x = 2 \end{cases},$ then $f$ is continuous at $x = 2,$ provided $\lambda$ is (where $[.]$ is the Greatest Integer Function).

Which one of the following functions is discontinuous at $x=1$?

The value of $k$ $(k > 0)$,for which the function $f(x) = \frac{(e^x - 1)^4}{\sin(\frac{x^2}{k^2}) \log(1 + \frac{x^2}{2})}$,where $x \neq 0$ and $f(0) = 8$,is continuous at $x = 0$,is

Let $f: R \rightarrow R$ be a continuous function satisfying $f(0)=1$ and $f(2x)-f(x)=x$ for all $x \in R$. If $\lim_{n \rightarrow \infty} \{f(x)-f(\frac{x}{2^n})\} = G(x)$,then $\sum_{r=1}^{10} G(r^2)$ is equal to

If $f(x) = \begin{cases} \frac{x-2}{|x-2|}+a & , x<2 \\ a+b & , x=2 \\ \frac{x-2}{|x-2|}+b & , x>2 \end{cases}$ is continuous at $x=2$,then $a+b=$

Prove that the function $f(x)=5x-3$ is continuous at $x=0$,$x=-3$,and $x=5$.