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Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by

$A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence}   x_{n} \rightarrow +\infty\right\}$

Then the set A is necessarily.

  1. $A$ connected set
  2. $A$ compact set
  3. $A$ singleton set 
  4. None of the above
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