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Need verification to solution for trig function limit question

  1. Jun 24, 2008 #1
    As I do not have the solution book and classes are over for the summer, I don't have any other way of verifying whether this is right or not.

    1. The problem statement, all variables and given/known data
    lim(x->0) (sin 4x) / (sin 6x)


    2. Relevant equations



    3. The attempt at a solution
    If I may temporarily remove the lim sign...
    [tex]\frac{sin 4x}{sin 6x} = \frac{sin4x}{4x} \times \frac{4x}{sin6x}[/tex]

    [tex] = \frac{sin4x}{4x} \times \frac{6x}{sin6x} \times \frac{4x}{6x}[/tex]

    By Limit Laws, take the limit of each fraction to get
    [tex]1 \times 1 \times \frac{4}{6}[/tex]

    4. Final answer
    2/3
     
  2. jcsd
  3. Jun 24, 2008 #2

    Defennder

    User Avatar
    Homework Helper

    You could also use L'Hopital rule to get the same result.
     
    Last edited: Jun 24, 2008
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