# Evaluate #lim_(x rarr -oo) sqrt(x^2 + x) - x #?

##
please show work :)

please show work :)

We know that

and, trivially,

Starting the proof, we set

and thus get

By completing the square, we find that this is the same as

and hence get

or

This shows that

and it follows that

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The limit of sqrt(x^2 + x) - x as x approaches negative infinity is 1/2.

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