Limit x -> 0 cos(x) - 1 / sin(x)

  • Thread starter smith007
  • Start date
  • #1
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Homework Statement


x in the following is actually Theta

Limit as x -> 0 (cos(x) - 1) / sin(x)



Homework Equations



none

The Attempt at a Solution



Multiply both sides by cos x +1

[ (cos x - 1) / sin x ] * [ (cos x + 1 )/ (cos x + 1)]

= [ cos2 x -1 ] / sin(x) (cos(x) +1)

= -sin2 x / sin x (cos x + 1)

- sin x / sin x cancels to -1 leaving sin x / (cos x + 1)

Sub in x -> 0

= (-1) (sin(0) / cos(0) + 1)

= (-1) (0/2) = 0


The only step I am not sure about the is cancelation of sin x /sin x. Is this allowed? How does the solution look?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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The solution looks fine. Sure you can cancel the sin(x)/sin(x).
 
  • #3
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Thank you for the fast response. Your help is much appreciated.
 

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