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 Jun25 awarded Informed Jun25 comment Example of a function of a convergent sequence with limit $l$ whose limit is not $f(l)$ Thanks a lot, your step-by-step was very helpful. I did end up with an answer in the end but through a much more convoluted method. Cheers! Jun25 accepted Example of a function of a convergent sequence with limit $l$ whose limit is not $f(l)$ Jun25 asked Example of a function of a convergent sequence with limit $l$ whose limit is not $f(l)$ Apr6 accepted Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$ Apr6 awarded Supporter Apr6 comment Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$ Ah yes of course, sorry. Clearly I shouldn't be doing this past midnight ... Apr6 comment Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$ I'm assuming by taking the sine of both sides? Thanks, this is a cool way to do it that I wouldn't have thought of straight away. Apr6 awarded Scholar Apr6 comment Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$ Ah gosh, I knew it was something horribly simple! My excuse is I'm a physics student and haven't done pure math for at least 2 years :P. Apr6 comment Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$ Sorry, the question is actually $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$, not $\frac{1}{n}\sin{\frac{1}{n}}$ (sorry, I realise that was a little confusing ...) Apr6 awarded Student Apr6 asked Squeeze theorem proof of $\lim_{n \rightarrow \infty} \sin{\frac{1}{n}}$