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Limit problem!

  1. Sep 10, 2006 #1
    I don't know if this neccessarily belongs in the calculus section, but it's for my calculus class.
    How would you go about finding the limit as x approaches 0 for
    (1-cos(x))/2sin^2(x)

    I know the answer is 1/4(unless I copied it down wrong :/ ) , but what first steps would you take to evaluating thing. Also this is for my review packet where we just know the basics of derivatives, so the only knowledge I should be going by are my trig identities and that the limit as x approaches 0 for sinx/x =1.
    Thanks.
     
    Last edited: Sep 10, 2006
  2. jcsd
  3. Sep 10, 2006 #2

    arildno

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    Expand your fraction by the factor (1+cos(x)).
     
  4. Sep 10, 2006 #3
    Thanks that helped out a lot, figured it out!
    I have a test on this chapter Tuesday, and these trig limits might just kill me.
    There are so many identities to use, so little time.
     
  5. Sep 10, 2006 #4

    arildno

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    Most of those trig identities can be opportunely RE-derived from a few simple facts:
    1. Sine is odd, cosine is even
    2. cos(x-y)=cos(x)cos(y)+sin(x)sin(y)
    3. cos^2(x)+sin^2(x)=1
    4 tan(x)=sin(x)/cos(x)

    Remembering those 4 is really all you need, along with skill at manipulating expressions.
     
    Last edited: Sep 10, 2006
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