My Math Forum Lim of sqrt (1-cos(x)) / x when x---> 0?

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 November 7th, 2009, 11:57 PM #1 Newbie   Joined: Nov 2009 Posts: 1 Thanks: 0 Lim of sqrt (1-cos(x)) / x when x---> 0? hi, i need to proof: lim sqrt (1-cos(x)) / x when x-->0. i think this limit is undefined, but i don't know how to prove it - without Le'Hopital's rule.. Thanks for your help!
 November 8th, 2009, 05:15 AM #2 Senior Member   Joined: Jun 2009 Posts: 150 Thanks: 0 Re: Lim of sqrt (1-cos(x)) / x when x---> 0? Another approach would use the (first two nonzero terms of) the Maclaurin series for cos(x) .
November 8th, 2009, 04:45 PM   #3
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Re: Lim of sqrt (1-cos(x)) / x when x---> 0?

Quote:
 Originally Posted by abypt hi, i need to proof: lim sqrt (1-cos(x)) / x when x-->0. i think this limit is undefined, but i don't know how to prove it - without Le'Hopital's rule.. Thanks for your help!
Another approach would be to multiply numerator and denominator by sqrt(1+cos(x)).
You end up with (sin(x)/x)/sqrt(1+cos(x)). You should have already sin(x)/x -> 1 as x->0

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# lim 무한대 루트 1-cosx

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