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[TEX]\Large \lim (\sqrt{n^2+2n+3}-n)=\lim \frac{2n+3}{\sqrt{n^2+2n+3}+n}=\lim\frac{2+\frac{3}{n}}{\sqrt{1+\frac{2}{n}+\frac{3}{n^2}}+1}=1[/TEX]
 
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