Question

Why when I do infinity/0, the answer given by the book is undefined, +infinity and -intfinity. I would have put undefined only...

Answer 1

I don't understand the question.
Are you asking why infty/0 = undefined and +infty-infty is undefined as well?

Answer 2

no... in my book the answer given to infinity/0 is undefined, +infinity and -infinity

Answer 3

but, I would have only put undefined

Answer 4

Well yes, both are undefined forms.

Answer 5

uh...? basically, my question is what does infinity/0 equal to?

Answer 6

why does my book say it also equals -infinity and +infinity

Answer 7

We don't know actually, That's why it is called "undefined".

Answer 8

yea... but my book says:\[\frac{ \infty }{ 0 } = +\infty, -\infty\] and undefined

Answer 9

in some very old math books something/0 was said to be = infinty

Answer 10

yeah, that being the old precalc books.
But if you have a grasp that any quantity divided zero is an undefined result, infinity by the other hand is unknown, so therefore it is not possible for it to be infnity.

Now, if the result would be a K/0 over a result that approaches zero from the denominator, then it is indeed infinity:
\[\lim_{x \rightarrow 2^+}\frac{ 1 }{ x-2 }=\frac{ 1 }{ 0^+ }=+ \infty\]

Answer 11

so the reason being that it's an older book?...

Answer 12

If the question is a limit as Owlcoffee mentioned then (in the case he mentions) the answer is infinity because the value never reaches 2 but gets a very very small quantity close to 2.
However if its say an algebra question and a denominator works out to 0 then then answer is undefined.