Notation Question: Understanding "y --> 2^(-) implies y < -2

[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 ??

 

[micromass]

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 $x<a$.

 

[chemistry1]

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

 

[micromass]

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

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

 

[chemistry1]

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

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