Question

Calculus help??????

Answer 1

$f(x)=\ln x\implies f'(x)=\dfrac1x$
$g(x)=x^2-1\implies g'(x)=2x$

You have $2x^2>1$ for all $x\ge1$, and dividing by $x$ gives $2x>\dfrac1x$, or $g'(x)>f'(x)$. By the racetrack principle, then, it follows that $g(x)>f(x)$.