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Math Help - Two Variable Limits

  1. #1
    Len
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    Two Variable Limit

    Let F(x,y)=\frac {x-y^4}{x^3-y^4}

    Determine whether lim(x,y)\rightarrow(1,1) F(x,y) exists.

    Any insight is appreciated, thanks.
    Last edited by Len; October 2nd 2008 at 07:27 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    ok, my first method remains valid, but the lines i chose were silly choices.

    again, approach the limit along y = x, you will find that the limit is 3

    but approach the limit along x = 2 - y^2, you will find that the limit is 3/5


    (i'm so used to approaching the origin, i said to approach along x = 0 without even realizing that we could never get close to the point (1,1) by doing that)
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  3. #3
    Len
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    This stuff is new to me so I'm trying my best to absorb it all, the help is really appreciated, thanks a lot.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Len View Post
    This stuff is new to me so I'm trying my best to absorb it all, the help is really appreciated, thanks a lot.
    well, keep practicing. this is one of those topics it takes a while to get, at least it did for me. i've forgotten a lot of the tricks that work with these though. this limit wasn't that bad
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  5. #5
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    I'm rusty at this stuff, but wouldn't some combination of partial derivatives and L'Hospital's rule work?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Prove It View Post
    I'm rusty at this stuff, but wouldn't some combination of partial derivatives and L'Hospital's rule work?
    perhaps, i have never actually used L'Hopital's rule in a multivariable case, so i can't say
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