- #1

Gib Z

Homework Helper

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## Main Question or Discussion Point

I just read the following fact and it somewhat defies my usual logic.

[tex]\lim_{x\to\infty} \sqrt{x^2+x} - x =\frac{1}{2}[/tex].

Now my usual logic tells me that as x becomes large, the leading term in a polynomial sequence is the major one and therefore the [itex]x^2+x[/itex] becomes [itex]x^2[/itex] so [itex]\sqrt{x^2+x}[/itex] becomes just x.

The same logic seems to work for this limit here:https://www.physicsforums.com/showthread.php?t=166906

However the limit is obviously not equal to zero, where is the error in this logic?

[tex]\lim_{x\to\infty} \sqrt{x^2+x} - x =\frac{1}{2}[/tex].

Now my usual logic tells me that as x becomes large, the leading term in a polynomial sequence is the major one and therefore the [itex]x^2+x[/itex] becomes [itex]x^2[/itex] so [itex]\sqrt{x^2+x}[/itex] becomes just x.

The same logic seems to work for this limit here:https://www.physicsforums.com/showthread.php?t=166906

However the limit is obviously not equal to zero, where is the error in this logic?