Question

Is there a function that resembles the \(\text{sqrt}\) function but whose limit as \(x\to\infty\) exists?

Answer 1

not sure what you mean by "resembles" the sqrt function but\[\large\lim_{n\to\infty}{n\over\sqrt[n]{n!}}=e\]

Answer 2

I am looking for something like this.

Answer 3

A function like the red one. That is, a function that converges as \(x\to\infty\), but whose inverse diverges as \(x\to\infty\).

Answer 4

what about \(y=e^{-x}\)?
doesn't that fulfill the requirement above?

Answer 5

That one will do. Thank you very much! :)

Answer 6

yay, I answered one of your questions finally ;)