Checking continuity of $f(x)=\ln(x)$

Question

Is $f(x) = \ln e$ continuous on the domain $D= (0,e]$ given that $0$ is not being included in the domain?

Graphically, it seems to be continuous.

Yes, the question asked was the original one only. Can you please edit it back. — LUCIFER, Sep 17 '17 at 20:30

score 2 · Answer 1 · answered Sep 17 '17 at 20:37

2

This function is a constant function; since $\ln e$ is another name for $1$, your function could be written $$ f(x) = 1. $$ Is that function continuous on the domain $(0, e]$? Sure. It's a constant function.

answered Sep 17 '17 at 20:37

John Hughes

93,729

score 0 · Answer 2 · answered Sep 17 '17 at 20:22

0

It's a continuous function because easy to prove that for all $a>0$ $$\lim_{x\rightarrow a}\ln{x}=\ln{a}$$

answered Sep 17 '17 at 20:22

Michael Rozenberg

194,933

Checking continuity of $f(x)=\ln(x)$

2 Answers2