- #1
Yuqing
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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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