Recent content by Noxerus

M is defined as the limit of g(x) when x \to c. L is defined as the limit of f(x) when x \to M. Both are written in the first paragraph of the first post. Intuitively, I'm trying to say that as x goes to c, g(x) goes to M. But, because as x goes to M in f(x), f(x) goes to L, I say that as x goes...

I would like to prove a chain rule for limits (from which the continuity of the composition of continuous functions will clearly follow): if \lim_{x\to c} \, g(x)=M and \lim_{x\to M} \, f(x)=L, then \lim_{x\to c} \, f(g(x))=L. Can someone please tell me if the following proof is correct? I am...

Thomas' Calculus.

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