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Math Help - convert it into polar coordinates,check limits

  1. #1
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    convert it into polar coordinates,check limits

    Hello,
    please try to do these questions.Thanks
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    Quote Originally Posted by m777 View Post
    Hello,
    please try to do these questions.Thanks
    There is adware embedded in this file.

    -Dan
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    Now i think so there is no adware in this file.i will attach it again.
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    Quote Originally Posted by m777 View Post
    Now i think so there is no adware in this file.i will attach it again.
    B) If the

    lim_{(x,y)->(0,0)} x y^3/(x^2+y^4)

    exists its value is independent of how (x,y) approaches (0,0).

    If we approach (0,0) along the x axis (x=0)

    lim_{(0,y)->(0,0)} 0*y^3/(y^4) = 0

    If we approach (0,0) along x=y

    lim_{(x,x)->(0,0)} x^4/(x^2+4^4) = 1.

    Therefore the limit does not exist.

    RonL
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  5. #5
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    Hello, m777!


    Convert .x^4 + 2x▓y▓ + y^4 - 6x▓y + 2y│ .= .0 . to polar coordinates.

    We have: .(x▓ + y▓)▓ - 6x▓y + 2y│ .= .0

    Then: .(r▓)▓ - 6(r▓Ěcos▓θ)(rĚsinθ) + 2(r│Ěsin│θ) .= .0

    . . . . . r^4 .= .6r│ĚsinθĚcos▓θ - 2r│Ěsin│θ

    Divide by r│: . r .= .6ĚsinθĚcos▓θ - 2Ěsin│θ

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Basically, we're done . . . it can be simplified a bit more . . .

    . . r .= .6Ěsinθ(1 - sin▓θ) - 2Ěsin│θ

    . . r .= .6Ěsinθ - 6Ěsin│θ - 2Ěsin│θ

    . . r .= .6Ěsinθ - 8Ěsin│θ

    . . r .= .2ĚsinθĚ(3 - 4Ěsin▓θ)

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