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

  • #1

Homework Statement


show that the limit as h approaches zero of ((cosh-1)/h) = 0.

Homework 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
 

Answers and Replies

  • #2
33,162
4,847
The author used this identity: cos(2x) = cos2(x) - sin2(x) = 1 - 2sin2(h), and then replaced 2x by h.
 
  • #3
Ah, I see. Thank you.
 

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