I know the answer to this problem, but I do not know how to get to it.

lim (sqrt(9x^2+x)-3x) = (1/6)

x-> infinity

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- Sep 14th 2008, 06:51 PMthecountthe limit as x approaches infinity
I know the answer to this problem, but I do not know how to get to it.

lim (sqrt(9x^2+x)-3x) = (1/6)

x-> infinity - Sep 14th 2008, 06:57 PMo_O
Multiply top and bottom by its conjugate: :

The numerator is an application of the difference of squares formula:

So:

etc. etc. - Sep 14th 2008, 07:01 PMskeeter

divide every term by x ...

now let - Sep 15th 2008, 02:06 PMMoo
Hello,

Another approach is to use asymptotic equivalences (but I don't know your level, so maybe you can't use it...)

Since , we have

So