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Homework Help: Proving: limit (as theta approaches zero) of sin(theta)/(theta) = 1

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data
    show that the limit as h approaches zero of ((cosh-1)/h) = 0.

    2. Relevant equations

    *The bold numbers preceding each line are simply line numbers, they are not apart of the equations.*

    1 lim (as h approaches 0) of ((cosh - 1)/h)

    2 = lim (as h approaches 0) of -((2sin2(h/2))/h)

    3 = -lim as theta approaches zero of ((sin[tex]\Theta[/tex]/[tex]\Theta[/tex])*sin[tex]\Theta[/tex]

    4 = -(1)(0)

    5 = 0



    I'm confused as to how the author of the text was able to get from line 1 to line 2. If someone could workout the steps between these two lines I would be appreciative. I'm drawing a blank here!

    Thanks
     
  2. jcsd
  3. Mar 8, 2010 #2

    Mark44

    Staff: Mentor

    The author used this identity: cos(2x) = cos2(x) - sin2(x) = 1 - 2sin2(h), and then replaced 2x by h.
     
  4. Mar 8, 2010 #3
    Ah, I see. Thank you.
     
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