What is $\lim_{n\rightarrow\infty}\frac{(n+1)^3}{(n+2)n^2}$? Having some trouble remembering limit calculations.
What is limit $$\lim_{n\rightarrow\infty}\frac{(n+1)^3}{(n+2)n^2}\ \text{?}$$

The idea is that only the highest powers matter in such cases. 
The proof is done by dividing both nominator and denominator by $n^3$ and seeing that most of the things like $3\cdot\frac{1}{n}$ or $\frac{1}{n^2}$  tend to $0$.
In general, divide by $n$ in highest power that exists in the denominator.
For example, to calculate the limit of $\frac{n^2+2n+3}{3n+5}$ divide the nominator and the denominator by $n$. To calculate the limit of $\frac{n^2+2n+3}{3n^2+5}$, divide both the nominator and the denominator by $n^2$.
