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Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one of the following is always true?

  1. The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a-} f(X)$ exist for all real number a
  2. if $f$ is differentiable at a then $f'(a)>0$
  3. There cannot not be a real number $B$ such that $f(x) < B$ for all real $x$
  4. There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$
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I think A is true but have doubt on B

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