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Math Help - How do you find the limit of this trig. function?

  1. #1
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    How do you find the limit of this trig. function?

    lim x-->0 [4x+sin(6x)]/[x-tan(5x)]
    x is theta

    I tried this:
    4/1 lim x->0 [x+sin(6x)]/[x-tan 5x]
    4/1 lim x->0 [x(1+[sin(6x)/x])/[x-(sin(5x)/cos(5x))]
    4/1 lim x->0 [x(1+[sin(6x)/x])/[x(1-[sin(5x)/x]*(1/cos(5x))]
    4/1 * 6/5 lim x->0 [1+(sin(6x)/6x)]/[(sin(5x)/5x)*(1/cos(5x))]

    I'm not sure if I did the steps right because I cannot seem to get the right answer.
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  2. #2
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    Quote Originally Posted by laila View Post
    lim x-->0 [4x+sin(6x)]/[x-tan(5x)]
    x is theta

    I tried this:
    4/1 lim x->0 [x+sin(6x)]/[x-tan 5x]
    4/1 lim x->0 [x(1+[sin(6x)/x])/[x-(sin(5x)/cos(5x))]
    4/1 lim x->0 [x(1+[sin(6x)/x])/[x(1-[sin(5x)/x]*(1/cos(5x))]
    4/1 * 6/5 lim x->0 [1+(sin(6x)/6x)]/[(sin(5x)/5x)*(1/cos(5x))]

    I'm not sure if I did the steps right because I cannot seem to get the right answer.
    Have you been taught l'Hopital's Rule?
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