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Thread: Graphs

  1. #1
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    Graphs

    For the graph x^3+y^3=1, why is there an asymptote at y=-x?

    Thanks.
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    -insert title here- Paradoxica's Avatar
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    Re: Graphs

    Consider the graph when x and y are very very large. (x+y)(x²-xy+y²)=1 ⇒ x+y = 1/(x²-xy+y²) ≈ 0 ⇒ x≈-y
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    617 pages fan96's Avatar
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    Re: Graphs



    When ,



    Which has no solution.

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    Re: Graphs

    making y the subject:
    y = (-x^3+1)^1/3
    factor out x^3
    =(x^3)^1/3 * (-1+1/x^3)^1/3
    =x (-1+1/x^3)^1/3
    as x becomes larger; the part with 1/x^3 becomes smaller and the graph of y=x (-1 + 1/x^3 )^1/3 gets closer and closer to the graph y=x(-1+0)^1/3 or y=-x. of course there will be no solutions but that is just because it's an asymtote and those never have solutions (take for example y=1/x which has an asymtote at y=0; yet one cannot arrive at a solution; same thing with y=e^x)

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