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Math Help - limits of severable variables

  1. #1
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    limits of severable variables

    1. does the limit (x+y)/(x^2-y^2) as (x,y) goes to (0,0) exist? If yes, find it. If no, show that it doesn't exist.

    = (x+y)/(x+y)(x-y)=1/(x-y). Doesn't exist. It can cancel as long as not at (0,0), and this is undefined. (I think I did this right, but can you give me an alternative reason?)

    2. Limit of x^2/y^2 as (x,y) goes to (0,0). Does it exist?
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  2. #2
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    1. If you travel along the path x=0, then you get -1/y. As y goes to 0 from the left, this approaches infinity. As y goes to 0 from the right, this approaches -infinity. Thus the limit does not exist.

    2. Along the path y=x the limit is 1. Along the path x=0 the limit is 0. So the limit doesn't exist.
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