You can. You get infinity, but you can. (You were thinking of L'Hospital right?)
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You can. You get infinity, but you can. (You were thinking of L'Hospital right?)
No, you don't get infinity. The limit from one side is negative infinity and from the other side is positive infinity - it fails to converge. At least under standard assumptions of how numbers and division work.
Edit: To elaborate, even if it did converge it would not actually be infinity unless it could be evaluated at that point; however, you'd have a decent case for it being a useful fiction. L'Hopital's doesn't really come into it.
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Hmmm....
If f(x) = 0, then f'(x) = 1, no?
So if we are dividing by the constant 0, ought L'Hôpital's Rule leave us entirely at the mercy of the numerator?
If f(x) = 0, then f'(x) = 1, no?
So if we are dividing by the constant 0, ought L'Hôpital's Rule leave us entirely at the mercy of the numerator?
If f(x) = 0, f'(x) = 0. I've not used L'Hopital's rule in a long time, but wiki says it only applies to cases where the limit of both numerator and denominator is either 0 or both infinity. For c/x the limit of the denominator x is 0, so L'Hopital's would only come in to play with 0 as the numerator. Which gives the thoroughly unexciting result of the limit of 0/x as x->0 being equal to the limit of 0/1 ie 0.
Wiki is usually good for maths, better than my old notes
Gah. You are right. This is what I get for trying to do basic calculus through nearly ten years of rust.
I remember the LotR-themed games, they were also divisible by five.
I wanted to take that one, but the list wasn't there yet.
But maybe I ought to claim it now.
I would like to claim game WWL CCCXXXIII
Dividing by 0 means a vertical line somewhere, right? I haven't taken calculus so this is the extent of my knowledge.
x*0=0. But 0/0=/=x unless x=0. x/0=0 though, but it's physically impossible because how do you divide x into 0 groups?
x*0=0. But 0/0=/=x unless x=0. x/0=0 though, but it's physically impossible because how do you divide x into 0 groups?
Yes the limit is plus or minus infinity and often the limit is what you look at. But it does happen in physics that you need to divide by 0 and then you get infinity. Just like dividing by infinity gives 0. Though luckily most of the time you need to divide by 0 you either expect to get infinity or the fraction is in a negative exponential function which then dies.
I thought you refered to L'Hospital when you said that sometimes you can divide by 0.
L'Hospital actually also works for infinity/0 and 0/infinity. In that case you either make the numerator 1/0 or 1/infinity or the denominator 1/0 or 1/infinity. I.e. infinity/0 is also infinity/(1/0)=infinity/infinity. And then you can differentiate the two functions and take the limit again to see whether or not you this time get either 0, infinity or something inbetween instead of something undefined. And c/0 indeed only involves L'Hospital in the special cases of c=0 or c=infinity; otherwise it is just infinity.If f(x) = 0, f'(x) = 0. I've not used L'Hopital's rule in a long time, but wiki says it only applies to cases where the limit of both numerator and denominator is either 0 or both infinity. For c/x the limit of the denominator x is 0, so L'Hopital's would only come in to play with 0 as the numerator. Which gives the thoroughly unexciting result of the limit of 0/x as x->0 being equal to the limit of 0/1 ie 0.
Wiki is usually good for maths, better than my old notes
And wiki indeed often is good for maths and physics.
I assume that is a number reservation?
That is correct, therefore I reacted to that particular post and made the number italic
If you plot it then dividing every term by 0 would give a vertical line---assuming you can get the plotting tool to actually want to draw it. But that normally isn't the point of dividing by 0. Most often you divide by 0 because you take a limit---and then you don't actually divide by 0---or you e.g. evaluate something at 0 temperature. And you far from always make a plot and even if you do then not all terms are necessarily divided by 0; and the division could be in the power of an exponential function. It could also be you wanted the value in 0 or the limit.Dividing by 0 means a vertical line somewhere, right? I haven't taken calculus so this is the extent of my knowledge.
0/0 could be x. And x/0 isn't 0, but infinity.x*0=0. But 0/0=/=x unless x=0. x/0=0 though, but it's physically impossible because how do you divide x into 0 groups?
The 0/0 limit you get from L'Hospital's rule.
I.e. if the fraction of of two functions in some limit is 0/0 or infinity/infinity and the fraction of the derivatives of those two functions exist in the same limit, then those two limits will be the same.
An example. Let f(x) = x^3 and g(x) = x. Then take f/g and take the limit of x -> 0. That is 0/0. So you employ L'Hospital. f'(x) = 3x^2 and g'(x) = 1. The limit of f/g as x -> 0 is then per L'Hospital equal to f'/g' in the limit of x -> 0, so you have that x^3/x = 0 in the limit of x-> 0. You could also have ended up with some finite number. And sometimes you end up with 0 in the denominator from L'Hospital; then it is infinity.
An example of where you frequently evaluate in 0 and thereby divide by 0 is partition functions.
For instance take the exponential part of the Grand Canonical partition function. I.e. e^(-beta(E-µN), where beta = 1/(k T). As the temperature T goes to 0 beta goes to infinity and the exponential vanishes. So if you evaluate it at 0 temeprature you indeed do divide by 0.
Go ahead!
I want the one after, though.
Erm, guys, what the hell?
As I pointed out before, there are people who asked to GM a Big quite some time ago. marty, you may feel that the list doesn't work, but that doesn't give you the right to just ignore it either.
I still don't get this list. It's said it's top first. I am top, and my time still hasn't came around. :unsure: