anonymous
  • anonymous
LIMIT SIN^2(X)/X(1+COS(X) AS X GOES TO 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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nikvist
  • nikvist
\[\lim_{x\rightarrow 0}\frac{\sin^2x}{x(1+\cos x)}\] is it correct?
anonymous
  • anonymous
YES
anonymous
  • anonymous
zero

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anonymous
  • anonymous
is the answer fairly sure
anonymous
  • anonymous
its not a indeterminate form , we can just sub in x=0
nikvist
  • nikvist
Ok, answer is 0, but this is indeterminate form 0/0
anonymous
  • anonymous
ahh yeh , im an idiot , didnt see the x factor on the bottom differnetiate top and bottom and try again
anonymous
  • anonymous
YES I GOT 0/0 BUT MY TEACHER MARK MY PAPER STILL WRONG WITH MY STEPS I JUST SUBSTITUTE X FOR 0
dumbcow
  • dumbcow
\[=\lim_{x \rightarrow 0}\frac{\sin x ^{2}}{x} * \lim_{x \rightarrow 0}\frac{1}{1+\cos x} = \lim_{x \rightarrow 0}2\sin x \cos x * \frac{1}{2} = 0\]
anonymous
  • anonymous
so [ 2sinxcosx ] / [ x(-sin(x) ) + (1+cos(x)) ] 2sin(x)cos(x) / [ 1 +cos(x) -xsin(x) ]
anonymous
  • anonymous
now when you sub x=0 , it isnt indeterminate , and we do get 0 as the final answer
nikvist
  • nikvist
dumbcow, \[\lim_{x\rightarrow a}f(x)g(x)\neq\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}g(x)\]
anonymous
  • anonymous
^doesnt it? I thought I remember reading somewhere that it does
dumbcow
  • dumbcow
really? are you sure lim x^2 as x->2 is 4 limx * limx as x->2 is 2*2=4
dumbcow
  • dumbcow
no they can be separated, see below http://tutorial.math.lamar.edu/Classes/CalcI/LimitsProperties.aspx
anonymous
  • anonymous
YES GUYS YOU CAN SEPARATE IM SURE OF THAT
anonymous
  • anonymous
before you answer, shut the caps button off LOL!
anonymous
  • anonymous
oh well ~

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