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 $\displaystyle \sqrt{x^2 + 9x + 1}$ can be expanded using the generalised binomial theorem.
Alternatively (and less rigorous) note that $\displaystyle \sqrt{x^2 + 9x + 1} = \sqrt{\left(x + \frac{9}{2}\right)^2 - \frac{77}{4}}$ ~ $\displaystyle \left|x + \frac{9}{2}\right|$.