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 \[\lim_{x \to a} f(g(x)) = f(b) = f\left(\lim_{x \to a} \; g(x) \right)\]

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