Question

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

Answer 1

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

Answer 2

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

Answer 3

since \(x\to2-\) then \(x<2\) so \(x-2<0\)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

I have tried it differently

at left as h tends 0 x tends\[2^{-}\]

Answer 10

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

Answer 11

and what solutions that?

Answer 12

you can put it and find it.