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How would I prove that the statement

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

is true/false?

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    $\begingroup$ 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? $\endgroup$ – Ethan Bolker Mar 13 at 13:12
  • $\begingroup$ so when n is large n^3 is also going to be large? sorry ive never used Θ before $\endgroup$ – lauren Mar 13 at 13:22
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$lim \frac{10n^{3}+3n}{n^3}$ 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)

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