Find the limit as x -> infinity of: (sqrt(x^2 + x) - x)

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MarkSA

Junior Member
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Sep 8, 2007
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243
Hello,

1) Find the limit as x -> infinity of: (sqrt(x^2 + x) - x)

I tried multiplying by the conjugate...

lim x->infinity of: (x)/(sqrt(x^2 + x) + x)

But I can't tell if that's in the form of 0/0 or infinity/infinity, so I can't use "the hospital" rule yet.

Is there an obvious way to get this into a form I can use the rule on? Thanks
 
o.k ... good job by multiplying the numerator and denominator of the original expression by the conjugate of \(\displaystyle \sqrt{x^2 + x} - x\) ... now you are at this point

\(\displaystyle \lim_{x \rightarrow \infty} \frac{x}{\sqrt{x^2+x} + x}\)

divide every term by x ...

\(\displaystyle \lim_{x \rightarrow \infty} \frac{1}{\sqrt{1+ \frac{1}{x}} + 1}\)

now let x get large ... do you see the limit now?
 
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