Consider the functions \(\rm f(x)=\frac{[x]}{x} \) & \(\rm g(x)=x[\frac{1}{x}]\) where \([\cdot]\) denotes the greatest integer less than or equal to x. Then which of the following is true?
1
\(\displaystyle \lim _{x \rightarrow 0}\) f(x) does not exist but \(\displaystyle \lim _{x \rightarrow 0}\) g(x) exist
2
\(\displaystyle \lim _{x \rightarrow 0}\) g(x) does not exist but \(\displaystyle \lim _{x \rightarrow 0}\) f(x) exist
3
\(\displaystyle \lim _{x \rightarrow 0}\) f(x) or \(\displaystyle \lim _{x \rightarrow 0}\) g(x) exists.
4
\(\displaystyle \lim _{x \rightarrow 0}\) f(x) does not exist but \(\displaystyle \lim _{x \rightarrow 0}\) g(x) does not exist