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2-var limit, find conditions for a,b,c watch

    • Thread Starter

    Problem: What condition must the constants a,b,c satisfy to guarantee that lim (x,y)->(0,0) xy/(ax^2 + bxy + cy^2) exists? Prove your answer.

    (Exercise 19 in Adams' Calculus 5th Edition, p. 717)

    Following either axis (x,0) or (0,y) shows that the limit is 0. I can show a lot of different relationships following different lines, such as x=+/-y, x=ry etc. But I can't come to the answer - I'm far from it to be honest.

    Thanks for any kind of help!

    If you don't want to read the answer do not read below.

    ((answer is a=c=0, b =/= 0.))
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Updated: February 28, 2006

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