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Limits of trig functions

  1. Jan 22, 2014 #1
    1.
    what would be the limit?? with out using the L'Hopital's rule

    lim_(x-0) (sin(3 x^2))/(8 x)


    the limit of sin(3x^2) divided by 8x as x approaches zero











    2. Limits of trignometric functions



    3. The attempt at a solution
    I tried factoring out the 1/8, but thats it, Idk how to go on


    Hope you can help me

    Thanks


     
  2. jcsd
  3. Jan 22, 2014 #2

    Dick

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    What's lim x->0 of sin(3x^2)/(3x^2)? That should be a good hint.
     
    Last edited: Jan 22, 2014
  4. Jan 22, 2014 #3


    1


    but how to put the 3x^2 below?
     
  5. Jan 22, 2014 #4

    Curious3141

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    What (expression) do you have to multiply 8x by to get 3x2? As long as you multiply both the top and bottom by the same, you don't change the fraction.
     
  6. Jan 22, 2014 #5
    3x on both numerator and denominator?
    i would get 24x^2, but i can split the fraction right?
     
  7. Jan 22, 2014 #6

    Curious3141

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    So you get ##\frac{3x\sin(3x^2)}{8(3x^2)}##. What happens next?
     
  8. Jan 22, 2014 #7


    We factor out.

    then the limx-0 of 3x/8 and limx-0 of sin(3x^2)/3x^2
    therefore

    limx-0 0*1
    so

    limx-0f(x)= 0
     
  9. Jan 22, 2014 #8

    Curious3141

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    Yes, exactly.
     
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