Solve this following


If $f(x)=[x]-\left[\frac{x}{4}\right], x \in R$, where $[x]$ denotes the

greatest integer function, then :


  1. Both $\lim _{x \rightarrow 4} f(x)$ and $\lim _{x \rightarrow 4+} f(x)$ exist but are not equal

  2. $\lim _{x \rightarrow 4-} f(x)$ exists but $\lim _{x \rightarrow 4+} f(x)$ does not exist

  3. $\lim _{x \rightarrow 4+} f(x)$ exists but $\lim _{x \rightarrow 4-} f(x)$ does not exist

  4. $\mathrm{f}$ is continuous at $x=4$

Correct Option: , 4


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