The right hand and left hand limit of the function are respectively.

$$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{e^{1 / x}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right.$$

$$\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }$$

If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x=0\end{array}\right.$$ is continuous at $$x=0$$, then the value of $$K$$ is

If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuous at $$x=0$$, then $$k=$$