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Math Help - please help

  1. #1
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    please help

    for which of the following values of c would we get
    Lim (Ln(cos cx))/ 2x^2 = -1 ?
    x->0

    <a>1
    <b> 2
    <c> 4
    <d> 8
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  2. #2
    Senior Member
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    There are several ways you could tackle this.

    L'Hopitals rule equates the limit of the ratio f/g with that of the derivatives f'/g' under suitable conditions on f and g. Here the derivative of log(cos(cx)) is -c.sin(cx)/cos(cx) and the derivative of 2x^2 is 4x. Using the well known limit of sin(x)/x, written as sinc(cx)/(cx) we have -c/(4/c) = -c^2/4. This is -1 for c=2.

    A numerical check: for x = 0.001, the ratio is -1.000001.
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