Hello, just joining up. Prof. Jerrison is very quick and engaging. I have a question about the proof that differentiability = continuity in lecture 2 (https://itunes.apple.com/us/podcast/lecture-01-derivatives-slope/id354869053?i=80690404) --- did I miss where it was shown that (the limit as x->z of a*b) is equal to (the limit as x->z of a)*(the limit as x->z of b)? The proof seems to hinge on that. It's certainly an intuitive inference, but is there a simple proof of said inference?
btw, the proof is the last few minutes of lecture 2 in the link referenced above.

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thanks for your replies guys, very helpful!

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