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## Main Question or Discussion Point

We often have

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

if f(x) is continuous at g(a).

But then my question arises where [tex]g(x)\rightarrow\infty[/tex]. I am not sure if there is any meaning to continuity at infinity as it seems that continuity is the property of a particular point. If the function is proven to be continuous for all x or at least for large x then will this equality hold?

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

if f(x) is continuous at g(a).

But then my question arises where [tex]g(x)\rightarrow\infty[/tex]. I am not sure if there is any meaning to continuity at infinity as it seems that continuity is the property of a particular point. If the function is proven to be continuous for all x or at least for large x then will this equality hold?

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