anonymous
  • anonymous
lim x->o (1-cosx)/x sqrt
Mathematics
katieb
  • katieb
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myininaya
  • myininaya
This seems to be a bit weird sqrt of what?
anonymous
  • anonymous
it's the new way...
anonymous
  • anonymous
lol

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

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