[MATH] Calculus Review Packet

[Newby]

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) = e^x
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.

[Sidoh]

[Chavo]

f(infinite + infinite) which = f(2*infinite), which could be f(2x);

2*infinity is just infinity

[Sidoh]

You guys both suck at spelling infinity.

[Chavo]

who what where? 

[Sidoh]

who what where? 

lol.  cheating bastard.

[Newby]

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!

[Sidoh]

Not to mention , and are undefined.

[dark_drake]

Not to mention . . . undefined.

Isn't it 0? I only ask because that's what we do in calculus.

[Chavo]

Not to mention . . . 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.

[dark_drake]

Not to mention . . . 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, .

[Rule]

?

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 . A constant over infinity is definitely zero, and even in rigorous mathematics we sometimes define 0 * infinity = 0 (and this is certainly less obvious).

[Chavo]

I must be thinking of something else.  I'm not a math nerd like certain other individuals around these parts

[Sidoh]

?

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 . 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 imply that the denominator is some arbitrary variable approaching infinity, then?

[Rule]

?

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 . 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 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.

[Sidoh]

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.

[Newby]

Not to mention . . . undefined.

Isn't it 0? I only ask because that's what we do in calculus.

Indeed.

[Sidoh]

Indeed.

Pff.  Just because I don't memorize little tables of data.