Big-O Notation of an expression

Asked Feb 05 '18 at 18:55

Active Feb 05 '18 at 19:03

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I have the expression $$ \frac{1}{A}\left(\ln x + \sqrt{2(\ln x-1)}\right),$$ where $A$ is a positive constant with respect to $x$.

I want to isolate the dominant term and add the error term in O-notation for $x \rightarrow \infty$.

Can someone give me a hint on how to approach this?

edited Feb 05 '18 at 19:03

abiessu

asked Feb 05 '18 at 18:55

N. Younger

2

Hints: $\sqrt{2(\ln x -1)}=\sqrt 2\cdot\sqrt{\ln x-1}$, $\sqrt{\ln x}-\sqrt{\ln x-1}\le 1$... – abiessu Feb 05 '18 at 18:57
@abiessu: So would you write $\frac{\ln x}{A} + O(\sqrt{\ln x})$? – N. Younger Feb 05 '18 at 19:01
That is what I would write, yes. – abiessu Feb 05 '18 at 19:01

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