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Need some help with this limits question

pineapplechemist

Hi guys i really need a hint as to what to do next here:

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Reply 1

Smaug123

Original post by pineapplechemist

Hi guys i really need a hint as to what to do next here:

"Choose \epsilon = \delta" is ambiguous. What is \delta here?

Your solution is going to need to start with "Let \epsilon be arbitrary." Indeed, you have to prove something "for every \epsilon".

Reply 2

pineapplechemist

Original post by Smaug123

"Choose \epsilon = \delta" is ambiguous. What is \delta here?

Your solution is going to need to start with "Let \epsilon be arbitrary." Indeed, you have to prove something "for every \epsilon".

How is this now?

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Reply 3

Smaug123

Original post by pineapplechemist

How is this now?

Yes, fine. "Continuous" means "change in f is small if change in x is small". "x_n tends to x" means "the change to get from x to x_n is small". Therefore, "the change in f is small when we go from x to x_n".