What Mistake Am I Making in This Limit Calculation?

[kLPantera]

Homework Statement

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

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]

Homework Statement

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

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
$$x^2 - x^2 + \frac{2x}{x} - r(x^2 + x),$$ (which IS the meaning of what you wrote) or whether you mean
$$x^2 - x^2 - \frac{2x}{x - r(x^2 + 2x)}$$
or
$$x^2 - \frac{x^2 + 2x}{x - r(x^2 + 2x)},$$
or several other possibilities.

RGV