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tamiashi
Group Title
Find the limit
lim {x>0} (1cos6x)/(x sin5x)
How to solve this?
 one year ago
 one year ago
tamiashi Group Title
Find the limit lim {x>0} (1cos6x)/(x sin5x) How to solve this?
 one year ago
 one year ago

This Question is Open

completeidiot Group TitleBest ResponseYou've already chosen the best response.0
are you allowed to use lhopital?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
everybody jumps for l'hospital... that should really be a last resort
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
is this\[\lim_{x\to0}{1\cos^6x\over x\sin^5x}\]?
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
I think it would make this easier to use l'hopitals rule for this on an exam though, just to save time.
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
Often you are not allowed to use l'hospital if the problem is\[\lim_{x\to0}{1\cos(6x)\over x\sin(5x)}\]it can be solved fairly easily without l'hospital. so far, however, @tamiashi has not replied to me, so I don't want to go ahead with either until I get a response.
 one year ago

tamiashi Group TitleBest ResponseYou've already chosen the best response.0
Sorry for being late in response, I'm not allowed to use L'hospital Can you show me how to solve it without L'hospital?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
is it the first way I wrote it or the second? are 5 and 6 exponents, or coefficients of the argument?
 one year ago

tamiashi Group TitleBest ResponseYou've already chosen the best response.0
it's the second way
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
first multiply by\[\frac{1+\cos(6x)}{1+\cos(6x)}\]
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
you then have\[{1\cos^2(6x)\over x\sin(5x)(1+\cos(6x))}=\frac{1\cos^2(6x)}{x}\cdot\frac1{\sin(5x)}\cdot\frac1{1+\cos(6x)}\]now multiply by \(\frac xx\) to get\[{1\cos^2(6x)\over x\sin(5x)(1+\cos(6x))}=\frac{1\cos^2(6x)}{x^2}\cdot\frac x{\sin(5x)}\cdot\frac1{1+\cos(6x)}\] manipluate this through trig identities and algebra sp that you can utilize\[\lim_{x\to0}\frac{\sin x}x=1\]to get your answer.
 one year ago

tamiashi Group TitleBest ResponseYou've already chosen the best response.0
okay got it now, thank you so much ^^
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
welcome :D
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.0
alternative : use the identity : sin^2 (3x) = (1cos(6x))/2 > 1  cos(6x) = 2 sin^2 (3x) so, it can be : dw:1361606909900:dw
 one year ago
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