# How to solve equations using big $\Theta$

How would I prove that the statement

$$10n^3 +3n = \Theta(n^3)$$

is true/false?

• Welcome to stackexchange. Hint: look at the definition of $\Theta$. What can yousay about the ratio of that function to $n^3$ when $n$ is large? – Ethan Bolker Mar 13 at 13:12
• so when n is large n^3 is also going to be large? sorry ive never used Θ before – lauren Mar 13 at 13:22

$$lim \frac{10n^{3}+3n}{n^3}$$ has a finite value, so I guess that's it (you will find M such that the left hand side of your equation would stay below M * the right hand side for a big every big enough n)