Which step am I doing wrong?

kLPantera · Sep 28, 2012

1. The problem statement, all variables and given/known data

limi as x-> positive infinity x+r((x^2)+2x)

3. The attempt at a solution

multiply by conjugate x-r((x^2)+2x)

I get (x^2)-(x^2)+2x/x-r((x^2)+2x)

Which becomes 2x/x-r((x^2)+2x)

Which I end up with 2/1-r(1-(2/x))

But I go wrong somewhere because I end up with 2/0 and the answer is positive infinity. I keep getting undefined and I can't see where I'm going wrong. Could someone point it out?

Ray Vickson · Sep 28, 2012

kLPantera said: ↑

1. The problem statement, all variables and given/known data

limi as x-> positive infinity x+r((x^2)+2x)

3. The attempt at a solution

multiply by conjugate x-r((x^2)+2x)

I get (x^2)-(x^2)+2x/x-r((x^2)+2x)

Which becomes 2x/x-r((x^2)+2x)

Which I end up with 2/1-r(1-(2/x))

But I go wrong somewhere because I end up with 2/0 and the answer is positive infinity. I keep getting undefined and I can't see where I'm going wrong. Could someone point it out?

What is r? Is it a number, a function, or what? If it is a number > 0 you should have no trouble saying what is ## lim_{x \rightarrow \infty} x + r(x^2 + x).## If r is a number < 0 it is almost as easy, but you need to be careful. And, of course, if r = 0 it is easier still.

I have no idea why you would want to take conjugates, and anyway, I stopped reading your work because you have not used brackets I cannot tell whether you mean
[tex] x^2 - x^2 + \frac{2x}{x} - r(x^2 + x),[/tex] (which IS the meaning of what you wrote) or whether you mean
[tex] x^2 - x^2 - \frac{2x}{x - r(x^2 + 2x)}[/tex]
or
[tex] x^2 - \frac{x^2 + 2x}{x - r(x^2 + 2x)},[/tex]
or several other possibilities.

RGV

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Which step am I doing wrong?

kLPantera

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