Evaluate the following limits. If needed, enter '101' for ∞ and '-101' for −∞.
$$\lim_{x \rightarrow \infty} \left( \sqrt{x^2 + 9 x + 1} -x \right)$$

Question

Evaluate the following limits. If needed, enter '101' for ∞ and '-101' for −∞.
$$\lim_{x \rightarrow \infty} \left( \sqrt{x^2 + 9 x + 1} -x \right)$$

anonymous · Answer

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anonymous · Answer

so the answer is ∞? @Easyaspi314

anonymous · Answer

Well, it happens to be that the limit approaches a finite number. It does not approach infinity.

It happens to be that it approaches 4.5.

anonymous · Answer

That can be seen graphically.

anonymous · Answer

Yea!!thats the answer!! but i still confused about how to do it

anonymous · Answer

Are you allowed a graphing calculator for exams?

anonymous · Answer

With a graphing calculator, it's so simple.

If you must do it without a calculator, then you must rationalize the numerator, algebraically, then take the limit of the new (equivalent) fraction, and you'll see it approaches 4.5

anonymous · Answer

the professor said we cant use a graphing calculater during the test :''(( is there any another way to calculate it?

anonymous · Answer

Read my last post.

anonymous · Answer

If you must see an algebraic solution, you can post that new question, asking for an algebraic solution, only. I will be back in a few minutes.

anonymous · Answer

Irecommend that you do work on the algebraic solution, as chances are, you will see such problem(s) on your exam. It is important.

anonymous · Answer

oh ok i am going to ask now haha

anonymous · Answer

ok..if no one responds when I return, I will go through it. But before posting the question, work on it yourself.

anonymous · Answer

ok thx