EPT
[h] weird calculus problem
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clazziquai
6685 Posts
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Darthdrunken
Germany50 Posts
S(x) is a function with lim x->a S(x)=S(a), and V(x)=S(x) for all x out of R except for a finite number of reals. For these changed values, lim x->a V(x)=/=V(a), but S(a), since there is some interval [b1,b2] with a out of [b1,b2], so no of the changed values except a is in the interval. On this interval, it's V(x)=S(x) for all x except a. And so lim x->a V(x)=S(a). Edited some misstyped things :p | ||
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Zortch
Canada635 Posts
lim x->a V(x)=S(x) | ||
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Cascade
Australia5405 Posts
If you dont get it solved by someone else, and you post the problem properly within an hour or so, ill help you out. EDIT: ok, so it seems like you got help...  | ||
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Klockan3
Sweden2866 Posts
Now the original S function is an analytic function which means that all limits are defined. Now the interesting part about limits is that they ignore discrete points, so even if an evil interstellar traveler did change a million of discrete points of S this is still true for all x: lim(x->a) S(x) = x^2. This is due to the fact that no matter how many discrete points you got you never got a line, and as such you can always get closer than any point you pick can get which means that a limit never touches any point at all, you need to redefine an interval to effect limits. It is the same thing in the first question, even if the new function is defined as 7 at the point x=5 you would still have the limit value of 25 at that point since the limit do not asses anything about the exact value at the point in question, just what the function around converges against. | ||
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clazziquai
6685 Posts
On September 22 2008 05:46 Cascade wrote: if you want help, cant you at least spend the time it takes to post the problem in your op, instead of making people download and open a .pdf? If you dont get it solved by someone else, and you post the problem properly within an hour or so, ill help you out. EDIT: ok, so it seems like you got help... Hey bro sorry man. I didn't think about that. I'll copy/paste for those who are curious about the problem. | ||
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clazziquai
6685 Posts
It is the same thing in the first question, even if the new function is defined as 7 at the point x=5 you would still have the limit value of 25 at that point since the limit do not asses anything about the exact value at the point in question, just what the function around converges against. What dose this mean? | ||
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Cascade
Australia5405 Posts
On September 22 2008 06:07 clazziquai wrote: Hey bro sorry man. I didn't think about that. I'll copy/paste for those who are curious about the problem. haha, ok. So for solution, I agree with the others: Changing the function at a finite number of points will not change any limits. Read up on the definiton of limits if this is not clear. If you want to take the problem further, here is another situation.  Seeing that you start with an analytic function, then redefines one point, then redefines a finite number (1 million) of points and nothing happens to the limits, what about changing the function in a countably infinite number of points? Will all limits still be the same always? or never? or sometimes? Can it happen that ALL limits change? Will limits get new values, or will they just not converge? gl hf. | ||
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Raithed
China7078 Posts
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clazziquai
6685 Posts
On September 22 2008 06:46 Raithed wrote: failed. Why do you always post stuff like this? lol | ||
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infinity21
Canada6683 Posts
The limit is what the value of the function is close to a point, not on it, so changing the value of that point makes no difference. Look at what the function is approaching, not the value of the function at that point. | ||
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