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November 8th, 2009, 12:57 AM   #1
 
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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!
abypt is offline  
 
November 8th, 2009, 06:15 AM   #2
 
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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) .
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November 8th, 2009, 05:45 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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