MHB Understanding Limits: Explaining Left and Right Limits in Simple Terms

[Poly1]

Could someone explain what things like \displaystyle \lim_{x \to 3^+}\frac{1}{x} and \displaystyle \lim_{x \to 3^-}\frac{1}{x} are supposed to be?

I googled and it gave me epsilon delta stuff. I'm not smart enough for that. (Doh)

I guess I'm asking if anyone could give a dumbed down explanation of sorts. :D

 

[Dustinsfl]

Could someone explain what things like \displaystyle \lim_{x \to 3^+}\frac{1}{x} and \displaystyle \lim_{x \to 3^-}\frac{1}{x} are supposed to be?

I googled and it gave me epsilon delta stuff. I'm not smart enough for that. (Doh)

I guess I'm asking if anyone could give a dumbed down explanation of sorts. :D

Plus means approaching 3 from the right so 3.1, 3.01, 3.001 etc
I bet you can guess what minus means.

 

[Poly1]

Why did you start with 3.1?

 

[Dustinsfl]

Why did you start with 3.1?

It isn't really a starting point. I was just emphasizing approaching from the right. We could start at 100 but the goal is to approach 3 and get really close to 3. Really close as in 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

 

[Poly1]

Thanks. Did I read that sometimes \lim_{x \to a^{+}}f(x) and \lim_{x \to a^{-}}f(x) can be different? How's that?

 

[Dustinsfl]

Thanks. Did I read that sometimes \lim_{x \to a^{+}}f(x) and \lim_{x \to a^{-}}f(x) can be different? How's that?

That is true. You can have jump discontinuities or one side going to neg inf and the other to pos inf.
Look at the Heaviside Function has an example

 

[Dustinsfl]

Here is an example you can try:
$$
\lim_{x\to 1}\frac{x^2 - 2x - 3}{x-1}
$$
You need to check the left and right limit.