# What is the limit of #(sqrt(x^2+x)-x) # as x approaches infinity?

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Jim H
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Feb 17, 2016

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The initial form for the limit is indeterminate

So, use the conjugate.

# = (x^2+x-x^2)/(sqrt(x^2+x)+x)#

# = x/(sqrt(x^2+x)+x)#

We know that

# = x/(xsqrt(1+1/x)+x)# #" "# (for# x > 0# )

# = x/(x(sqrt(1+1/x)+1))#

# = 1/(sqrt(1+1/x)+1)#

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