Calculus

Find the limit: lim x-> 2 ln(x/2)/ (x^2−4)

Can someone help me with this?

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  1. I thought that it was 1/4 but that's now the answer....

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  2. What I thought that I had to do was to take the derivative, (2/x)/2x and then plug in 2... and that's how I got 1/4, but that's not the answer, what do I have to do?

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  3. D'hôpital's rule works here.
    The expression is
    ln(x/2)/ (x^2−4)

    not
    2ln(x/2)/ (x^2−4)
    as it appears in the post.

    The leading 2 belongs to the limit of x.

    Differentiate both top and bottom with respect to x:
    Lim (1/x) / (2x)
    = lim 1/(2x²)
    =1/(2(2)²)
    =1/8

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