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## Homework Statement

I want to find the following limit, ## \lim_{x \rightarrow \infty } x( \sqrt{ x^{2} +9} -x) ##, without using the Laurent series

## Homework Equations

None.

## The Attempt at a Solution

I used the Laurent Series to expand the square root, giving ## x((x+\frac{9}{2x})-x)##, then giving the limit as ##\frac{9}{2}## . How would one go about this question without using the above method?