IMathAS-libretexts

What word or phrase best completes the sentence below?

"If

\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}\ne{L}

, then we can find an

\displaystyle \epsilon>{0}

so that no matter how close

\displaystyle {x}

is to

\displaystyle {a}

$\displaystyle {f{{\left({x}\right)}}}$ will be within $\displaystyle \epsilon$ units of $\displaystyle {L}$ .
$\displaystyle {f{{\left({x}\right)}}}$ will be at least $\displaystyle \epsilon$ units away from $\displaystyle {L}$ .
it is possible for $\displaystyle {f{{\left({x}\right)}}}$ to be at least $\displaystyle \epsilon$ units away from $\displaystyle {L}$ .
$\displaystyle {f{{\left({x}\right)}}}$ will be getting farther from $\displaystyle {L}$ .
$\displaystyle {f{{\left({x}\right)}}}$ will never equal $\displaystyle {L}$ .