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find if limit exists: lim(x,y)->(0,0) [6(x^3)y]/[2(x^4) + (y^4)]

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find if limit exists: lim(x,y)->(0,0) [6(x^3)y]/[2(x^4) + (y^4)]

Mathematics
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whhy
Hold one of the variables constant, for example (x,0) -->(0,0) lim 0/2x^4. It suggests the limit is 0. This is the answer your instructor is looking for (although it doesn't necessarily prove it; it requires more rigorous work to prove it.) Knowing that info, you can say the limit is zero.

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i think there is another answer maybe? b/c it doesn't matter whether you put x = 0 or y = 0 it will equal 0
That strengthens the argument the lim is zero. There are infinitely many ways to approach the (0,0) and you have established at least two of them. If the answers were different it would prove that the limit does not exist.
  • M
okay thanks. i thought i was supposed to munipulate the equation and find that the limit doesn't exists.
It is an open question: may be it exists may be not. The interesting about this is it is not continuous (x,y) can not be 0. However, you can still find the lim because you are studying it as it gets closer and closer to 0 even though it doesn't get there. (In this case, the equation can not be manipulated further.)

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