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Math Help - Multi-Variable Limit Problem

  1. #1
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    Multi-Variable Limit Problem

    Question...

    (x,y) = (4x) / (1x+5y)
    lim (x,y)→(0,0)

    What is the limit along the line y=mx


    My Attempt
    The function then becomes...

    (x,mx) = (4x) / (1x+5mx)
    lim (x,mx)→(0,0)

    I thought the answer was then as easy as dropping all the variables and seeing that approaching the origin the function is closest to 4/6, but this is incorrect.

    What am I not understanding?
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Multi-Variable Limit Problem

    First, don't forget that:
    (mx)^2 = m^2x^2

    Why would you "drop" the variables? You have (4x) / (1x+5mx) = (4x) / [(1+5m)x] = 4/(1 + 5m)
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  3. #3
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    Re: Multi-Variable Limit Problem

    Quote Originally Posted by TheChaz View Post
    First, don't forget that:
    (mx)^2 = m^2x^2
    Don't I feel stupid! Totally forgot my parenthesis. I had tried the answer 4/(1+5m) and when it wasn't correct I assumed the problem was more than a silly distribution error. Thanks for the help, that's what I was looking for!
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  4. #4
    Super Member TheChaz's Avatar
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    Re: Multi-Variable Limit Problem

    No problemo.
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