I think you did a good job! However there were a few mistakes with putting a ‘c’ in place of an ‘a’. Also, I think in relation to what you’re proving, for style at least, it would be better to have written “l(x) is continuous *at a*”; as in your proof you’d sometimes only written “l(x) is continuous” with no domain specified.

As Greg mentioned there were a few problems with notation in your original proof that came up more than once. This was a bit misleading because I was not sure if you meant to introduce a new variable or not, so I would just be a bit more cautious when writing a proof. Also, you used the algebraic limit theorem without specifying why you could use it or what the theorem actually states which could strengthen your proof. Overall great job though!

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