how do I read this correctly

[kory]

If I'm approaching zero from the left then how is the answer 1?
If I'm approaching zero from the right then how is the answer -1?

Sorry. Forgot to add the graph...

 

[nasi112]

If you go to the zero from the left side, where will you arrive?

 

[Dr.Peterson]

If I'm approaching zero from the left then how is the answer 1?
If I'm approaching zero from the right then how is the answer -1?

It's hard to see how you could not consider it obvious. Perhaps it will help if you explain what other answer you get, and how.

Are you looking at the graph like this?

 

[kory]

Ok...After looking at your arrows I was able to see it more clearly. I just see dots so its not as clear to me as it is to you guys...

 

[pka]

kory, do you see that \(h(2))\) does not exist( not defined)? BUT \(\mathop {\lim }\limits_{n \to 2} \left( {h(x)} \right) = 2~?\)
If \(x\in\) a left-hand neighborhood of zero is \(h(x)\approx 1~?\)
If \(x\in\) a right hand neighborhood of zero is \(h(x)\approx -1~?\)
Thus \(\mathop {\lim }\limits_{\delta x \to {0^ - }} h(x) = 1\quad \& \quad \mathop {\lim }\limits_{\delta x \to {0^ + }} h(x) = - 1\)

 

[kory]

Got it. Thanks pka. I'm sure I'll have another dumb question for you soon lol.

 

[Dr.Peterson]

Ok...After looking at your arrows I was able to see it more clearly. I just see dots so its not as clear to me as it is to you guys...

The arrows are what limits are all about. You need to learn to draw your own arrows (or just move your eyes, or your finger, over a graph to think about how the function behaves. Although modern definitions are all about epsilons and deltas and proofs, the original ideas of calculus are about motion, and it's important to be able to imagine that motion.

That's one benefit of in-person teachers or videos, where you can see how the teacher is thinking as he moves points around.

 

[kory]

Do any of you have a discord? I'd like to hear some of your explanations in real time.