# Approximating when variable to infinity

In a book on algorithms I read that $$n^2 (1+\log n)$$ as $$n$$ approaches infinity is approximated to $$n^2 \log n$$.

I am not sure if I understand reasoning in this. Is it because $$1+\log n$$ grows so fast that $$\log n$$ could substitute it, so that +1 makes no big difference and so is ignored?

Yes, for large $$n$$ you can consider for all practical purposes that $$n^2 (1+ \log n) \approx n^2 \log n$$. Is is like you say, as $$n$$ increases the +1 becomes more and more insignificant (to quantify how insignificant, you can compute the relative error).