Clan x86
General Forums => Academic / School => Topic started by: Newby on October 24, 2006, 11:58:17 pm
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I need help.
If f(x1) + f(x2) = f(x1 + x2), for all real numbers x1 and x2, which of the following could define it?
A. f(x) = x + 1
B. f(x) = 2x
C. f(x) = 1 / x
D. f(x) = ex
E. f(x) = x2
The answer is B. But how would I prove that? I tried plugging in infinite for x1 and x2, and got f(infinite + infinite) which = f(2*infinite), which could be f(2x); is that right? Or are my math skills shit? :p
EDIT -- After looking over my review packet, I realized plugging in random numbers was not this one; it was some limit that I was not sure about.
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(http://latex.sidoh.org/?render64=JCQkZih4KT0yeFxcXFwNCmYoeF8xK3hfMik9Mih4XzEreF8yKT0yeF8xKzJ4XzI9Zih4XzEpK2YoeF8yKSQkJA==)
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f(infinite + infinite) which = f(2*infinite), which could be f(2x);
2*infinity is just infinity
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You guys both suck at spelling infinity.
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who what where? :-*
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who what where? :-*
lol. cheating bastard.
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f(infinite + infinite) which = f(2*infinite), which could be f(2x);
2*infinity is just infinity
Yeah. Today I realized it was dumb.
And it turns out I had to pick through the answers and try each one. so eh! :)
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Not to mention (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D), (http://latex.sidoh.org/?render=e^{\infty}) and (http://latex.sidoh.org/?render=\infty^{2}) are undefined. ;)
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Not to mention (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D). . . undefined.
Isn't it 0? I only ask because that's what we do in calculus.
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Not to mention (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D). . . undefined.
Isn't it 0? I only ask because that's what we do in calculus.
Pretty sure its undefined. Back when I took calc2, we always used 'no solution' as the answer to any problem that winded up with a 1/infinity in it.
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Not to mention (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D). . . undefined.
Isn't it 0? I only ask because that's what we do in calculus.
Pretty sure its undefined. Back when I took calc2, we always used 'no solution' as the answer to any problem that winded up with a 1/infinity in it.
According to wikipedia, (http://upload.wikimedia.org/math/7/8/f/78f15f7290a30f9d30972f90193209e2.png).
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?
So if you were asked what the limit of a/x is, as x --> infinity, you would write 'undefined'? That's horrible, and wrong: your teacher should be disciplined :P. A constant over infinity is definitely zero, and even in rigorous mathematics we sometimes define 0 * infinity = 0 (and this is certainly less obvious).
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I must be thinking of something else. I'm not a math nerd like certain other individuals around these parts :P
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?
So if you were asked what the limit of a/x is, as x --> infinity, you would write 'undefined'? That's horrible, and wrong: your teacher should be disciplined :P. A constant over infinity is definitely zero, and even in rigorous mathematics we sometimes define 0 * infinity = 0 (and this is certainly less obvious).
No, I would write 0. Does (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D) imply that the denominator is some arbitrary variable approaching infinity, then?
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?
So if you were asked what the limit of a/x is, as x --> infinity, you would write 'undefined'? That's horrible, and wrong: your teacher should be disciplined :P. A constant over infinity is definitely zero, and even in rigorous mathematics we sometimes define 0 * infinity = 0 (and this is certainly less obvious).
No, I would write 0. Does (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D) imply that the denominator is some arbitrary variable approaching infinity, then?
It depends. Most people who write 1/infinity mean more precisely lim y--> infinity 1/y, so the answer is "yes" in most cases. However, I think saying "yes" for all cases would be over-restrictive, unless we add all sorts of conditions about the "rate" of approaching infinity, etc. Regardless of whether you think of infinity as some 'closed entity' (for lack of a better term) or not, (and some would argue that this is a bad interpretation, although I think it does have some merit), we can see that in this particular case 1/'infinity' and lim x--> infinity 1/x are equivalent, as both equal zero.
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It depends. Most people who write 1/infinity mean more precisely lim y--> infinity 1/y, so the answer is "yes" in most cases. However, I think saying "yes" for all cases would be over-restrictive, unless we add all sorts of conditions about the "rate" of approaching infinity, etc. Regardless of whether you think of infinity as some 'closed entity' (for lack of a better term) or not, (and some would argue that this is a bad interpretation, although I think it does have some merit), we can see that in this particular case 1/'infinity' and lim x--> infinity 1/x are equivalent, as both equal zero.
Yeah, that's sort of what I would have guessed.
In any case, can you elaborate on the "closed entity" or does it require a heavy background in mathematics that I don't have (yet)? It sounds like an interesting concept.
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Not to mention (http://latex.sidoh.org/?render=%5Cfrac%7B1%7D%7B%5Cinfty%7D). . . undefined.
Isn't it 0? I only ask because that's what we do in calculus.
Indeed.
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Indeed.
Pff. Just because I don't memorize little tables of data. :P