Q4

Consider the following statement about real numbers: “Whichever positive number $r$ you pick, it is possible to find a number $x$ greater than $1$ such that $\frac{\ln x}{x^3}<r$.” When this statement is written in the formal language of proof, which of the following is obtained?

A. $\forall x>1\;\exists r>0\;\frac{\ln x}{x^3}<r$
B. $\exists x>1\;\forall r>0\;\frac{\ln x}{x^3}<r$
C. $\forall r>0\;\exists x>1\;\frac{\ln x}{x^3}<r$
D. $\exists r>0\;\forall x>1\;\frac{\ln x}{x^3}<r$