$(2$ marks$)$ Use the definition of "big Oh$"$ to prove that $\frac{(3n+4)}{(n^2+2)}$ is $O(\frac{1}{n})$

$(2$ marks$)$ Let $f_1(n),f_2(n),g_1(n),$ and $g_2(n)$ be positive functions. If

$f_1(n)$ is $O(g_1(n))$ and $f_2(n)$ is $O(g_2(n)),$ using the definition of "big Oh$"$

show that $f_1(n)*f_2(n)$ is $O(g_1(n)*g_2(n))$