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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?

A) The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a-} f(X)$ exist for all real number a

B) if $f$ is differentiable at a then $f'(a)>0$

C) There cannot not be a real number $B$ such that $f(x) < B$ for all real $x$

D) There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$
asked in Calculus by Boss (17.6k points) | 61 views

1 Answer

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I think A is true but have doubt on B
answered by Boss (17.6k points)

A is not always true.

Consider the graph below. It is strictly increasing but discontinuous at x=2.

B is always true.

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