anonymous
  • anonymous
evaluate limit as x goes to 2 = sin(x-2)/(x^2-4)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
infinity
anonymous
  • anonymous
take the limit of top and bottom sin(0) = 1 (2^2 - 4) aproaches 0 BUT can never go to zero because you cant divide by zero
anonymous
  • anonymous
so as the denominator goes to 0.00000001 or 0.000000000000000001

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anonymous
  • anonymous
its ilike this 1/4 then 1/2 then 1/1 then 1/0.000001 then 1/0.0000000000001
anonymous
  • anonymous
This one can be handled with a little manipulation. The bottom can be expanded to (x-2)(x+2). The lim of [sin (x-2)]/(x-2)]=1. That leaves 1/(x+2). So lim is 1/4.
anonymous
  • anonymous
no the bottom cannot be expanded like that
anonymous
  • anonymous
I am guessing by the way these questions are set up that x^2-4 is not sin of, but just a number.
anonymous
  • anonymous
I think the its sin of x-2 so sin(x-2)
anonymous
  • anonymous
divided by x^2 - 4
anonymous
  • anonymous
In that case we are saying the same thing. \[x ^{2}-4=(x-2)(x+2)\]The difference of two squares.
anonymous
  • anonymous
no thats what you are saying
anonymous
  • anonymous
that is impossible to do
anonymous
  • anonymous
I have had a couple beers. But are you telling me that the above is not the difference of two squares?
anonymous
  • anonymous
no it is
anonymous
  • anonymous
maybe your right im sorry
anonymous
  • anonymous
limit as x goes to 2 = sin(x-2)/(x^2-4) 0/0 so Use L'Hopital's rule lim x->2 Cos(x-2)/(2x) = Cos (0) / (2*2) = 1/4

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