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Math Help - proving limit doesn't exist

  1. #1
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    proving limit doesn't exist

    I'm having problems with some questions on a calculus worksheet. The main one is:

    'Show that the following limit does not exist:

    lim x+y/x-y
    (
    x,y)->(0,0)


    I think to prove that a limit doesn't exist you have to use the 'Two-Path test' although i'm not sure how to do this. Any help would be much appreciated. Thanks.

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  2. #2
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    Quote Originally Posted by herandi1 View Post
    I'm having problems with some questions on a calculus worksheet. The main one is:

    'Show that the following limit does not exist:

    lim x+y/x-y


    (
    x,y)->(0,0)


    I think to prove that a limit doesn't exist you have to use the 'Two-Path test' although i'm not sure how to do this. Any help would be much appreciated. Thanks.
    Approach along the x-axis (y=0) and then approach along the y-axis (x=0). You'll get two different limits.
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  3. #3
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    im confused, do we need to bring in a constant with these functions, otherwise it'll still make 0/0 right?
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  4. #4
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    Quote Originally Posted by herandi1 View Post
    im confused, do we need to bring in a constant with these functions, otherwise it'll still make 0/0 right?
    Just say that the limit does not exist. 0/0 is meaningless.
    Along the path y=-x the limit is 0.
    Along the path y=0 the limit is 1.
    That proves that there is no limit.
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  5. #5
    Junior Member woof's Avatar
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    Quote Originally Posted by herandi1 View Post
    im confused, do we need to bring in a constant with these functions, otherwise it'll still make 0/0 right?
    Simplify before you take the limit.

    For y=0: \ \ {x\over x}=1 and then take the limit, which is 1.

    For x=0: \ \ {-y\over y}=-1 and then take the limit, which is -1.
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