$vv$ Details

$(10$pts$)$ Let $f(x)=3x^3+5x^2+36x+64$ and $g(x)=x^3.$

a$)$ Prove directly from the definition of big $O$ that $f(x)$ is $O(g(x)).$ Use the approach and format shown in lecture. That means your $\text{'}C\text{'}$ should end up equal to $6.$

b$)$ Prove that $f(x)$ is $O(g(x))$ by taking a limit$.$

c$)$ Is $f(x)(g(x))?$ Prove your answer.

d$)$ Is $f(x)(g(x))?$ Prove your answer.

e$)$ Is $f(x)(g(x))?$ Prove your answer.