# What Mistake Am I Making in This Limit Calculation?

• kLPantera
In summary: XZlcnkgdGhlIGZ1bmN0aW9uIGlzIGEgbnVtYmVyID8gSSBzaG91bGQgdGhpcyB3YXMgYSBudW1iZXIgPzogSG9uZyBvZiB0aGlzIHdvcmsgYmVmb3JlIHRvIHJlcXVpcmUgYSBub3JtYWxpemUgdG8gY2FsbCB3aXRoIGl0LiBUaGlzIGlzIGludGVuZGVkIGludG8gdGhlIGZ
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?

kLPantera said:

## 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

## 1. Why am I not getting the expected results for my experiment?

There could be several reasons for this: 1) You may have missed a crucial step in the experimental procedure. 2) Your equipment or materials may be faulty. 3) Your hypothesis may be incorrect. 4) There may be external factors affecting your results. It is important to carefully review your experimental procedure and make any necessary adjustments.

## 2. How do I know if I am following the correct steps in my experimental procedure?

It is important to carefully read and follow the procedure outlined in your experiment. You can also consult with a mentor or colleague to ensure you are on the right track. Another helpful tip is to double-check your steps and compare them to the expected results to see if they align.

## 3. What should I do if I realize I have skipped a step in my experiment?

If you realize you have skipped a step, it is important to stop and go back to complete the missed step before continuing with the experiment. Skipping a step can significantly impact your results and may lead to inaccurate conclusions.

## 4. How do I troubleshoot if my experiment is not working?

If your experiment is not working, the first step is to carefully review your procedure and check for any errors or missed steps. You can also try repeating the experiment or adjusting any variables that may be affecting the results. It may also be helpful to consult with a mentor or colleague for troubleshooting advice.

## 5. What can I do if I am unsure about a specific step in my experimental procedure?

If you are unsure about a specific step, it is important to consult with a mentor or colleague for clarification. You can also do some additional research or refer to reliable sources to better understand the step. It is important to have a clear understanding of the procedure before proceeding with the experiment.

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