If $f(x) = \begin{cases} e^{1/x}, & x \ne 0 \\ 0, & x = 0 \end{cases}$,then:

If $f(x) = |x - b|,$ then the function:

If the function $f: R \rightarrow R$ defined by $f(x) = \begin{cases} \frac{a(1-\cos 2x)}{x^2}, & x < 0 \\ b, & x = 0 \\ \frac{\sqrt{x}}{\sqrt{4+\sqrt{x}}-2}, & x > 0 \end{cases}$ is continuous at $x = 0$, then $a+b=$

The value of $f(0)$ so that the function $f(x) = \frac{2^x - 2^{-x}}{x}$ for $x \neq 0$ is continuous at $x = 0$ is:

If $f(x) = \begin{cases} x, & \text{if } x \text{ is irrational} \\ 0, & \text{if } x \text{ is rational} \end{cases}$,then $f$ is

The function $f(x) = [x]^2 - [x^2]$,(where $[y]$ is the greatest integer less than or equal to $y$),is discontinuous at