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Math Help - Limit Rules

  1. #1
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    Limit Rules

    I am having some challenges understanding this problem, I was wondering if someone could help me understand how to approach it?
    thank you in advance

    Suppose that:

    L (a) = lim as x -> 0 of (a^x -1)/x

    Exists or all a > 0. Assume also that lim x -> 0 a^x =1.

    Using limit rules, prove that:

    L(ab) = L(a) + L(b)

    for a,b> 0

    Hint: (ab)^x -1 = a^x(b^x - 1) + (a^x - 1)
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  2. #2
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    Re: Limit Rules

    Hey brharrii.

    Have you tried just evaluating the limits for L(a), L(b) and L(ab)?
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  3. #3
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    Re: Limit Rules

    Hi Chiro,

    Thanks for the response. I'm not all the way sure how I to do that. To be honest I'm not sure that I understand the question completely. I understand the concept of a limits, but this question is quite a bit different from the ones I've been working on in the past. I'm used to solving limits where there is only 1 variable. How Can this problem be evaluated with so many variables? (a, b, x)

    Thanks!
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  4. #4
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    Re: Limit Rules

    Given an expression for L(x) sub in x = a, x = b, and x = ab and then show that LHS = RHS (in terms of L(ab) and L(a), L(b)).
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