najwaischua
lim x->o (1-cosx)/x sqrt
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myininaya
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This seems to be a bit weird sqrt of what?
dpaInc
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it's the new way...
FoolForMath
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lol
Kreshnik
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LOL @myininaya I thought It was \[\LARGE \lim_{x\to 0}{1-\cos x \over \sqrt x}\]
najwaischua
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the lower is
x^2
Kreshnik
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\[\LARGE \lim_{x\to 0}{1- \cos x\over x^2}\] ?
najwaischua
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yes yes
myininaya
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do you l'hospital?
myininaya
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i mean know?
najwaischua
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yes. but the question say use limit rule. don't use l'opitall's rule
najwaischua
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i've tried to use factorization. but can't get it
myininaya
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ok \[\lim_{x \rightarrow 0}\frac{1-\cos(x)}{x^2} \cdot \frac{1+\cos(x)}{1+\cos(x)}\]
\[\lim_{x \rightarrow 0}\frac{1-\cos^2(x)}{x^2(1+\cos(x))}=\lim_{x \rightarrow 0}\frac{\sin^2(x)}{x^2(1+\cos(x))}\]
need more help?
myininaya
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\[\lim_{x \rightarrow 0}\frac{\sin(x)}{x} \cdot \lim_{x \rightarrow 0}\frac{\sin(x)}{x} \cdot \lim_{x \rightarrow 0}\frac{1}{1+\cos(x)}\]
najwaischua
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the answer should be?
myininaya
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so you got this right ?
najwaischua
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actually no. what technique is this?
myininaya
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you wanted to use algebra and limit laws...
myininaya
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do you have any questions with the steps i performed?
niki
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is the ans 1/2?
Kreshnik
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you're supposed to know this rule:
\[ \lim_{x\to0}{\sin x\over x}= ?\] what should be instead of "?"
najwaischua
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Kreshnik
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so there's nothing to get confused of :) .. @myininaya solved it, you just had to substitute :)
najwaischua
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thank you