Notation question

1. Jul 9, 2014

chemistry1

Hi,

I have a question about : http://imgur.com/RU7PvtJ

I actually understand what I need to do. I need to see if both one sided limits are the same to establish that the limit exists. The only thing which I just find weird is the "since y --> 2^(-) implies y<-2"

Can somebody explain me where this y --> 2^(-) is coming from ??

2. Jul 9, 2014

micromass

Staff Emeritus
It is just a notation to denote the left-hand limits. So

$$\lim_{x\rightarrow a^-} f(x)$$

is the limit of $f(x)$ as $x\rightarrow a$ but $x<a$.

3. Jul 9, 2014

chemistry1

But shouldn't we say : y --> -2^(-) and not y --> 2^(-) ???

4. Jul 9, 2014

micromass

Staff Emeritus
Yes, you are correct. The book is wrong there (and it is wrong is the same place on the next line too).

5. Jul 9, 2014

chemistry1

Yes, I also noticed it. Ok, thank you!