IMathAS-libretexts

Which of the following are true statements? Mark all that are true.

$\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}$ and $\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}$ and $\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}.$
$\displaystyle \lim_{{{x}\to{a}}}{f{{\left({x}\right)}}}={0}$ and $\displaystyle \lim_{{{x}\to{a}^{+}}}{f{{\left({x}\right)}}}={0}$ implies that $\displaystyle \lim_{{{x}\to{a}^{{-}}}}{f{{\left({x}\right)}}}={0}.$

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