0 votes 0 votes Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one of the following is always true? The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a-} f(X)$ exist for all real number a if $f$ is differentiable at a then $f'(a)>0$ There cannot not be a real number $B$ such that $f(x) < B$ for all real $x$ There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$ Calculus isi2016 functions + – Tesla! asked Apr 30, 2018 • edited Nov 8, 2019 by go_editor Tesla! 864 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes I think A is true but have doubt on B Tesla! answered Apr 30, 2018 Tesla! comment Share Follow See all 2 Comments See all 2 2 Comments reply Kushagra Chatterjee commented Apr 30, 2018 reply Follow Share A is not always true. Consider the graph below. It is strictly increasing but discontinuous at x=2. 1 votes 1 votes Kushagra Chatterjee commented Apr 30, 2018 reply Follow Share B is always true. 1 votes 1 votes Please log in or register to add a comment.