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| Math Central | Quandaries & Queries |
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Question from Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function |
Hi Rahul,
I think the result you want is
If $f$ is continuous at $b$ and $\lim_{x \rightarrow a} \; g(x) = b$ then
\[\lim_{x \to a} f(g(x)) = f(b) = f\left(\lim_{x \to a} \; g(x) \right)\]
Penny
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