math question (limits)

Shouldn''t it be infinity?
If x = 1, f(x) = 1
If x = 0.1, f(x) = 100
If x = 0.01, f(x) = 10000
etc.

~~~~~~~~~~
Martee
http://www.csc.uvic.ca/~mdill

i just found in another book i have

lim x->2 1/(x-2)^2

it says "we see that the limit equals infinite. thus, the limit does not exist".

??


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Infinity exists
Actually, I think it''s accepted to say either "infinity", or "it doesn''t exist". I have seen both for the same functions.

~~~~~~~~~~
Martee
http://www.csc.uvic.ca/~mdill

nm, i get it now. i just asked some1.
it''s both "does not exist" and "infinite"
but it''s not "undefined" because it''s defined as "infinite"

heh,weird stuff

i''m gonna fail my calc ap test !!

thuned

life is unfair, take advantage of it.
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I suppose they say "does not exist" because infinity is not a real number, but I''d still write the answer as infinity.

-Ironblayde
 Aeon Software

Down with Tiberia!
"All your women are belong to me." - Nekrophidius

lim 1 x->0 --- = +i i=infinity x^2

If you were to read this out loud it would say "The limit, as x approaches zero, of 1 over x squared, is plus infinity."
If we were to try to divide by zero, we would get an undefined number.
When you take limits, x does not actually become 0, it just gets really, really close, infinitessimly close. as x gets smaller and smaller, x^2 gets smaller and smaller, and 1/(x^2) gets bigger and bigger. So, as x gets closer and closer to 0, 1/(x^2) gets closer and closer to infinity.

We can take this in the opposite direction.

1 lim --- = 0 x->+i x^2

As x gets bigger and bigger, 1/(x^2) gets smaller and smaller, until it reaches zero. A limit is just that, the point where it can go no further.

Are you even trying to be intelligent?
'cuz if you are, it ain't workin'
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Edited by - capn_midnight on April 9, 2001 1:04:28 PM

Well, if you have been studying limits for very long, you should know that the limit only exists if the limit from the right approaches the same number as the limit from the left.

If you take the limit from the right going left to zero, then the limit would approach infinity. However, if you take the limit from the left (negative) going towards zero, then the limit would approach negative infinity.

That is why the limit does not exist, not because the limit from the right approaches infinity, but because the limit from the right and the limit from the left do not approach the same number.

quote:

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Original post by Ranok

Well, if you have been studying limits for very long, you should know that the limit only exists if the limit from the right approaches the same number as the limit from the left.

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That is true, but it does not apply here. The denominator is a squared term (x²) and thus is always positive. The limit is positive infinity regardless of whether you approach x=0 from the left or the right, thus the limit is infinity.

-Ironblayde
 Aeon Software

Down with Tiberia!
"All your women are belong to me." - Nekrophidius