Can ns ask because that the limit as $x$ approaches $\lim_x \to 0-\ln x$? you re welcome explain. Its because since the limit of a role only exist if the lim as $x$ ideologies some number $n$ indigenous both the confident and negative side is the same, ns not sure that im persuaded that the limit together $x$ philosophies $0$ because that $\ln x$ exists. I understand its an unfavorable infinity indigenous the positive side, yet from the negative side?  The domain the $\ln(x)$ is just positive reals, so the left-hand limit at 0 doesn"t really make sense.

You are watching: Limit of ln x as x approaches 0 For a limit to exist, the two borders approaching from the left and also right side require to match up.

I.e. We need $$\lim\limits_x\to0^-\ln(x) = \lim\limits_x\to0^+\ln(x)$$ to it is in true.

Since $\ln(x)$ is not defined for $x\leq 0$ assuming us are assessing over the reals, the left-hand border can"t be evaluated, and also thus the limit does not exist.

If friend are analyzing over the facility numbers, that"s a somewhat various story, yet given her wording, I"ve assumed the we"re talking around the reals here. Thanks for contributing solution to medtox.orgematics ridge Exchange!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; earlier them up with referrals or personal experience.

Use medtox.orgJax to style equations. Medtox.orgJax reference.

See more: Everything You Know About The Constitution Is Wrong, Everything You Know About Constitution Is

## Not the prize you're spring for? Browse various other questions tagged limits or ask your own question.

Calculating this limit: $\lim_n\to\infty\;n\cdot\sqrt\frac12\left(1-\cos\frac360^\circn\right)$ site architecture / logo © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.18.40487

her privacy

By click “Accept every cookies”, girlfriend agree ridge Exchange can store cookies on your device and disclose info in accordance with our Cookie Policy.