The other comments are correct: 
is undefined. Similarly, the limit of 
as 
approaches 
is also undefined. However, if you take the limit of 
as 
approaches zero from the left or from the right, you get negative and positive infinity respectively.
The other comments are correct: is undefined. Similarly, the limit of as approaches is also undefined. However, if you take the limit of as approaches zero from the left or from the right, you get negative and positive infinity respectively.
does tend to 
as you approach zero from the left, and 
as you approach from the right:
That these limits are not equal is why 
is undefined.
Videos
Like 10/2- imagine a 10 square foot box, saying 10 divided by 2 is like saying “how many 2 square foot boxes fit in this 10 square foot box?” So the answer is 5.
But if you take the same box and ask “how many boxes that are infinitely small, or zero feet squared, can fit in the same box the answer would be infinity not “undefined”. So 10/0=infinity.
I understand why 2/0 can’t be 0 not only because that doesn’t make and since but also because it could cause terrible contradictions like 1=2 and such.
Ah math is so cool. I love infinity so if anyone wants to talk about it drop a comment.
Edit: thanks everyone so much for the answers. Keep leaving comments though because I’m really enjoying seeing it explained in different ways. Also it doesn’t seem like anyone else has ever been confused by this judging by the comment but if anyone is I really liked this video https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:division-zero/v/why-dividing-by-zero-is-undefined
$$\frac{x^2-2x}{x^2-2x+1}=\frac{x(x-2)}{(x-1)^2}\xrightarrow[x\to1]{}-\infty$$
since $\;x(x-2)\to-1\;$ and $\;(x-1)^2\to 0^+\;$ (meaning: approximates to zero from the positive side), so your limit is negative infinity.
Some may define this as "the limit doesn't exist", but I think it is more accurate to say "the limit doesn't exist finitely" and/or "the limit exists in the wide sense of the word", " the function diverges to $\;-\infty\;$", or something similar.
There's certainly nothing illegal about the form. It may be a nonsensical expression, but so far, no law has been acepted that prohibits it.
If you get $\frac{-1}{0}$ as the result, then the limit can either not exist or be equal to $-\infty$ or $\infty$. For example, the limit $$\lim_{x\to 0}\frac{1}{x}$$
does not exist, while the limit$$\lim_{x\to0}\frac1{x^2}$$ is equal to $\infty$.
Well... yes and no. It depends on the context in which you set yourself.
For example, consult the operations with the infinity element of the Riemann Sphere: https://en.wikipedia.org/wiki/Riemann_sphere#Arithmetic_operations
(Note that on the Riemann Sphere, also the real projective line, you don't make a difference between $-\infty$ and $+\infty$.)
In simple $\mathbb{R}$, where infinity is not an accepted element, this doesn't work, because you're exiting your base set. It's like trying to prove that $-2$ is a natural number, since $5 - 7 = -2$. However, this is not how $\mathbb{N}$ works: $-$ is not a closed operator in $\Bbb N$.
Who told you that $\frac{1}{0}$ is $\infty$ !!
This expression is simply undefined as division by zero is undefined.
However following is correct
$\displaystyle\lim_{x \to 0^+}\frac{1}{x}=\infty$
As you already said in question that
$\displaystyle\lim_{x \to -\infty}10^{-x}=0$
then how can you say that $10^{-\infty}=0$. Both the expressions are different.
When solving limits i found that when you reach 0/0 you have to cancel terms to find a real number when substituting c into the equation, is the new real number answer the correct response for the limit?
If so when you substitute c into a limit and it equals 1/0 for example, does this limit not exist and equal either or -infinity or + infinity, or would you have to cancel terms out and solve for a real number just like an indeterminate form?
My main question is when do you give up trying to get a real number from a limit that equals either 0/0, 1/0 or infinity/0. do you only solve for a real number when its indeterminate form?