I want to disprove $0.01n^3+ 0.0000001n^7$ is $O(n^3)$ and this is how I started.
The following is my proof:
Proof by Contradiction: assume the statement is true.
Then $0.01n^3+ 0.0000001n^7 < cn^3$ for some $c>0$ and for all $n>$1.
but after this point I got stuck. I honestly don't know what to do after this! Any help or hints would be appreciated!