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I am not sure how this method is called in english, but when can I use $$\lim_{x\rightarrow 0} \frac{\sin(x)}{x} = 1$$

and all the other known limits to solve other unknown limits?

Peter
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Zuzana Mitterová
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    Thank you for the edit good sir. – Zuzana Mitterová May 06 '17 at 22:53
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    You can always use it, except when you can't. ;-) Just joking: what's the question anyway? – egreg May 06 '17 at 22:57
  • @egreg Now that was funny. – Mark Viola May 06 '17 at 23:01
  • What are "known limits" and "unknown limits" ? Please clarify and specify your problem! – Peter May 06 '17 at 23:06
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    I can't name the method in english. It's when you are solving a limit and there is a set of limits that you know what they equal to, like the one I used in the description. And you are trying to get your problem to look like these known limits so you can say that part of it is equal to 1. There are also the 1-expx/x equals 1 when x approaches 0 etc. – Zuzana Mitterová May 06 '17 at 23:45
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    The answer was indeed "Always, except when you can't". –  May 07 '17 at 01:40
  • @ZuzanaMitterová You don't care about idiot's comment. $\sin x≒x$ is important in physics, too and these are useful when you compute the limit or their limits are used to easy practice. – Takahiro Waki May 07 '17 at 03:20
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    It is advisable to use such well known limits to solve typical limit problems and you can always use them in context of evaluation of limits. While this method may not always work (in few cases) , it is the method which requires least mathematical machinery. Once you are familiar with this approach, you may learn the highly powerful technique of Taylor series and L'Hospital's Rule (which is also powerful, but has challenges of its own). – Paramanand Singh May 07 '17 at 04:03

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