Daedalus Posted May 21, 2012 Share Posted May 21, 2012 (edited) #7 refers. If you calculate (8-x^3)/(2-x) when x=2 you get 0/0. However I want to watch a TV prog now so I'll just say I make this example of 0/0 equal to 12. If anyone doubts this then I'll come back later. We can use L'Hopital's rule to verify the accuracy of your statement: [math]f(x)=8-x^3[/math] [math]g(x)=2-x[/math] such that: [math]F(x)=\frac{f(x)}{g(x)}[/math] where: [math]\lim_{x \to 2} \frac{f(x)}{g(x)} \ = \ \lim_{x \to 2} \frac{f'(x)}{g'(x)} \ = \ \lim_{x \to 2} \frac{-3\, x^2}{-1} \ = \ \frac{3 \times 2^2}{1} \ = \ 12[/math] Note: In most cases, L'Hopital's rule can be used to determine the limit of indeterminate forms - [math]\frac{0}{0}[/math] and [math]\frac{\infty}{\infty}[/math]. However, this is getting off-topic and it would be better to start a thread in the mathematics forum discussing indeterminate forms. Edited May 21, 2012 by Daedalus Link to comment Share on other sites More sharing options...
Joatmon Posted May 21, 2012 Share Posted May 21, 2012 Okay, but why does it equal 12? [math] (12*x)/x [/math] ? If you aren't familiar with calculus you can still see that this result is extremely likely to be true by making x= to a tiny bit more than 2 and then x=to a tiny bit less than 2. One results in a bit more than 12 and one results in a bit less than 12. If you plot different values of x from(say) x=1 to x=3 and include those plots close to x=2 you will get a curve that obviously indicates 12 on the Y axis when x=2. If interested and you have not yet done calculus give it a try - have fun! Link to comment Share on other sites More sharing options...
studiot Posted May 21, 2012 Share Posted May 21, 2012 Hello morgsboi, You don't need calculus to understand when you can arrive at a proper value for zero/zero/ or infinity / infinity. Take a look at the expressions I showed in your other thread about this. Can you see that in the one case the top and bottom of the fraction gets smaller and smaller the more terms you add and in the other (which is called an infinite product) the top and bottom gets larger and larger? Link to comment Share on other sites More sharing options...
morgsboi Posted May 21, 2012 Author Share Posted May 21, 2012 Hello morgsboi, You don't need calculus to understand when you can arrive at a proper value for zero/zero/ or infinity / infinity. Take a look at the expressions I showed in your other thread about this. Can you see that in the one case the top and bottom of the fraction gets smaller and smaller the more terms you add and in the other (which is called an infinite product) the top and bottom gets larger and larger? Yes, thanks you. Link to comment Share on other sites More sharing options...
studiot Posted May 22, 2012 Share Posted May 22, 2012 (edited) Here is the second fraction rewritten: [math]\frac{1}{2}*\frac{3}{3}*\frac{4}{4}*\frac{5}{5}*\frac{6}{6}...... = \frac{1}{2}[/math] Can you see that no matter how far we go along the product, taking the same number of terms top and bottom, all the terms cancel except the first, so we are left with a half? So in this case (different numbers would yield different answers) [math]\frac{\infty }{\infty }[/math] evaluates to 1/2. When I first met this sort of thing an older wiser bear said to me "There are many infinities" "How so?" I asked " How else would infinity/infintity come out at so many different answers?" he growled. go well Edited May 22, 2012 by studiot Link to comment Share on other sites More sharing options...
swansont Posted May 22, 2012 Share Posted May 22, 2012 ! Moderator Note Since the OP has been answered ("No", insofar as the OP makes any sense) and the rest of the discussion is pretty much the same as http://www.scienceforums.net/topic/66527-0-paradox/ , this is closed Link to comment Share on other sites More sharing options...
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