What hapeens if the limit is being taken from the left?

Question

across · Answer

Anything can happen, but generally, you're approaching the limit point from negative infinity.

anonymous · Answer

so in a problem such as $$\lim_{x \rightarrow 2-}\frac{ x^2+4 }{ x-2 }$$ howw would it work?

helder_edwin · Answer

since $x\to2-$ then $x<2$ so $x-2<0$

helder_edwin · Answer

this means that
$$ \Large \lim_{x\to2-}\frac{x^2+4}{x-2}=-\infty $$

anonymous · Answer

ok, so i won't have to plug anything in?

anonymous · Answer

and if it were moving to the right it would be  $$+\infty$$

helder_edwin · Answer

well, pluging in you would have
$$ \Large \frac{2^2+4}{2-2}=\frac{8}{0} $$

helder_edwin · Answer

yes. if $x\to2+$ then $x>2$ so $x-2>0$

pradipgr817 · Answer

I have tried it differently
|dw:1347746473941:dw|
at left as h tends 0 x tends$$2^{-}$$

pradipgr817 · Answer

so if we replace x by 2-h and let h tends to 0 then there will be a different solution.

anonymous · Answer

and what solutions that?

pradipgr817 · Answer

you can put it and find it.