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tamiashi
 2 years ago
Find the limit
lim {x>0} (1cos6x)/(x sin5x)
How to solve this?
tamiashi
 2 years ago
Find the limit lim {x>0} (1cos6x)/(x sin5x) How to solve this?

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completeidiot
 2 years ago
Best ResponseYou've already chosen the best response.0are you allowed to use lhopital?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3everybody jumps for l'hospital... that should really be a last resort

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

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3Often 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.

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

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

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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3you 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.

tamiashi
 2 years ago
Best ResponseYou've already chosen the best response.0okay got it now, thank you so much ^^

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