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How do i get rid of the zero factor ?

  1. Dec 6, 2013 #1
    1. The problem statement, all variables and given/known data

    lim (sinθ-1/2)/(θ-∏/6)
    θ→∏/6

    2. Relevant equations



    3. The attempt at a solution
    Direct substitution with ∏/6 gives 0/0
    How do i get rid of the zero factor ?
     
  2. jcsd
  3. Dec 6, 2013 #2

    jedishrfu

    Staff: Mentor

    You can't that why they want you to find the limit at that point.

    You must use other means what does your textbook say about finding limits?
     
  4. Dec 6, 2013 #3

    ShayanJ

    User Avatar
    Gold Member

    You can use L'Hôpital's rule.
     
  5. Dec 6, 2013 #4
    My text book explained using limθ→0 sinθ/θ =1, using trigonometric identites and multiplying by the conjugate (in case of algebraic expressions) to solve limits.
    This question was in the differentiation section but it's before L'Hopital Rule so I guess there must be some other way.
     
  6. Dec 6, 2013 #5

    jedishrfu

    Staff: Mentor

    You could transform it to something similar using phi = theta - pi/6 to get

    lim phi->0 sin(phi + pi/6) / phi
     
  7. Dec 6, 2013 #6

    ShayanJ

    User Avatar
    Gold Member

    Maybe the identity [itex] \sin{\alpha}-\sin{\beta}=2 \sin{\frac{\alpha-\beta}{2}} \cos{\frac{\alpha+\beta}{2}} [/itex] helps.
    Also have in mind the more general formula [itex] \lim_{x\rightarrow 0} \frac{\sin{ax}}{bx}=\frac{a}{b} [/itex]
     
    Last edited: Dec 6, 2013
  8. Dec 6, 2013 #7

    jedishrfu

    Staff: Mentor

    Shyan great hint...
     
    Last edited: Dec 6, 2013
  9. Dec 6, 2013 #8

    ShayanJ

    User Avatar
    Gold Member

    you...and more...Nemo's are welcome!!!

    ;)
     
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