rpearson345
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# Calculus help?????? the functions f(x)= ln(x) and g(x)= x^2-1 they are both 0 when x=1 apply the Race Track Principle to explain which of the following inequalities is true for x is (greater than or equal to) 1: f(x) < g(x) or g(x) < f(x)

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