Whats the text meant to say by comparison with |x-2| slower faster thing? [closed]

calculus derivatives

I'm really not sure what the question is. It seems possible that the question is what does it mean to say one function tends to zero faster than another.

Def. Suppose $\lim_{x\to2}f(x)=\lim_{x\to2}g(x)=0$. We say $f\to0$ "faster than" $g$ as $x\to2$ if $\lim_{x\to2}f(x)/g(x)=0$.

So if $f(x)\to0$ faster than $x-2$ as $x\to2$ then the definition of the derivative says exactly that $f'(2)=0$.

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