Monday, 11 April 2016

limits - Evaluating and proving limlimitsxtoinftyfracsinxx

I've just started learning about limits. Why can we say lim even though \lim_{x\rightarrow \infty} \sin x does not exist?



It seems like the fact that sin is bounded could cause this, but I'd like to see it algebraically.



\lim_{x\rightarrow \infty} \frac{\sin x}{x} = \frac{\lim_{x\rightarrow \infty} \sin x} {\lim_{x\rightarrow \infty} x} = ?



L'Hopital's rule gives a fraction whose numerator doesn't converge. What is a simple way to proceed here?

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