evaluate

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

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

help?

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- Sep 29th 2009, 02:03 PMB-lapLimits
evaluate

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

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

help? - Sep 29th 2009, 02:28 PMpickslides
My attempt would be,

$\displaystyle \lim_{x \to \infty} \sqrt{x^2+9 x+1} = \sqrt{\infty^2+9\times\infty+1} = \sqrt{\infty} = \infty

$ - Sep 30th 2009, 01:18 AMmr fantastic
Note that $\displaystyle \sqrt{x^2 + 9x + 1}$ can be expanded using the generalised binomial theorem.

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