## haterofmath 2 years ago What hapeens if the limit is being taken from the left?

1. across

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

2. haterofmath

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

3. helder_edwin

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

4. helder_edwin

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

5. haterofmath

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

6. haterofmath

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

7. helder_edwin

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

8. helder_edwin

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

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

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

11. haterofmath

and what solutions that?