JackOfAll
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 2d comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) I'm not following what you did there, Apr12 accepted Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) Apr12 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) How did you introduce that division step? (Step 2 to Step 3) Apr12 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) I don;t understand how that can be the solution, yet, the manual implies it's much more direct and obvious. Single worst "solution" I have ever seen in a book. You're just supposed to know how to split up the fraction like that? Apr12 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) No clue what the tilda deal is, but there is no way that original explanation intended there to be any real work, or bizarre notation. Thanks for trying. Apr12 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) What enrages me about the original explanation is that is so off-handedly implies the connection is obvious, and requires no actual work. There is no way in hell they intended the reader to be deriving all this stuff in these replies. Sadly, I still have absolutely no idea how lim sin(x)/x has anything to do with the 6x/2x problem. Sigh. Can someone please just spell it out for me, and please don't leave the last step out, all cute so I can finish. This has dragged on way longer than it should. Apr12 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) Sorry, that was a typo. I corrected the correct solution above. Apr12 revised Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) edited body Apr10 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) I am not following the solution, and am more interested in understanding the explanation given in the OP. It is written as if that limit makes the answer obvious with almost no work. Did they skip a major leap? I have no idea how to connect the original problem to $\lim_{x\to 0}\frac{\sin(x)}{x}=1$ Apr10 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) I am not following the solution, and am more interested in understanding the explanation given in the OP. It is written as if that limit makes the answer obvious with almost no work. Did they skip a major leap? I have no idea how to connect the original problem to $\lim_{x\to 0}\frac{\sin(x)}{x}=1$ Apr10 comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) I am not following the solution, and am more interested in understanding the explanation given in the OP. It is written as if that limit makes the answer obvious with almost no work. Did they skip a major leap? I have no idea how to connect the original problem to $\lim_{x\to 0}\frac{\sin(x)}{x}=1$ Apr9 asked Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital) Apr7 comment P(bowling a strike) = 70%. Expected number of trials until a perfect game? (10 strikes in a row) Yup, I was missing ()'s for the numerator. Struck down by PEMDAS!! Apr6 comment P(bowling a strike) = 70%. Expected number of trials until a perfect game? (10 strikes in a row) Marcus, your formula doesn't seem to work right. I plugged it into Excel, and for p=.5 and n=1, I get 5 trials. For p=.5 and n=2, I get 9 trials. Those both seem wrong. Apr6 comment If odds of an event is $80\%$, how many events needed until you get $n$ consecutive events? Did, is this the same answer as what you formulated? math.stackexchange.com/questions/1218810/… Apr4 accepted P(bowling a strike) = 70%. Expected number of trials until a perfect game? (10 strikes in a row) Apr4 comment P(bowling a strike) = 70%. Expected number of trials until a perfect game? (10 strikes in a row) Thanks Marcus so much for your great explanation. I will try to rederive your work, and then use the formula on a few examples. Apr3 asked P(bowling a strike) = 70%. Expected number of trials until a perfect game? (10 strikes in a row) Apr2 awarded Favorite Question Mar19 comment If odds of an event is $80\%$, how many events needed until you get $n$ consecutive events? What is wrong with this approach? Can't you think of the 30 days as 1 chunked event?