[tex]\\ \lim_{n \to \infty} \ln{ (2n^2+1) }-\ln{(n^2+1)}
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\\ \lim_{n \to \infty} \ln{ \frac{2n^2+1}{n^2+1} }
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\\ \lim_{n \to \infty} \ln{ \frac{ \frac{2n^2}{n^2} + \frac{1}{n^2}}{ \frac{n^2}{n^2}+ \frac{1}{n^2}} }
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\\ \lim_{n \to \infty} \ln{ \frac{ 2 + \frac{1}{n^2}}{ 1+ \frac{1}{n^2}} }
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\\ \ln{ \frac{ 2 + 0}{ 1+ 0} }
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\\ \ln{2}[/tex]
