Is the following true? Is so, under what conditions, and what are, roughly, the arguments used to prove it?(adsbygoogle = window.adsbygoogle || []).push({});

f,g two functions of superiorly unbounded domain and such that for x > N, g(x) is continuous and f(g(x)) is continuous.

[tex]\lim_{x \rightarrow \infty} f(g(x)) = f(\lim_{x \rightarrow \infty} g(x))[/tex]

I'm trying to show what

[tex]\lim_{x \rightarrow \infty} ln \left(\frac{x-1}{x+1} \right)=0[/tex]

where ln is the natural logarithm (I think some people use the notation log for that). And without that "theorem", I don't see how to do it.

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# Is this proposition true?

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