Limits

**B-lap** · September 29th 2009, 02:03 PM

evaluate
lim x->infinity square root (x^2+9x+1)

I tried 0, -1, 1, Infinity, and neg. infinity and none were correct.
help?

**pickslides** · September 29th 2009, 02:28 PM

My attempt would be,

$\lim_{x \to \infty} \sqrt{x^2+9 x+1} = \sqrt{\infty^2+9\times\infty+1} = \sqrt{\infty} = \infty<br />$

**mr fantastic** · September 30th 2009, 01:18 AM

Originally Posted by B-lap

evaluate
lim x->infinity square root (x^2+9x+1)

I tried 0, -1, 1, Infinity, and neg. infinity and none were correct.
help?

Note that $\sqrt{x^2 + 9x + 1}$ can be expanded using the generalised binomial theorem.

Alternatively (and less rigorous) note that $\sqrt{x^2 + 9x + 1} = \sqrt{\left(x + \frac{9}{2}\right)^2 - \frac{77}{4}}$ ~ $\left|x + \frac{9}{2}\right|$ .

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