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Math Help - find intersections without calculator

  1. #1
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    find intersections without calculator

    How would I find complex intersections without the intersection function on the calculator.

    Say I have y=4xe^(-x^2) and y = |x|. How would I find this intersection.

    Note. I really only need the x values because I am trying to then find the area between these two curves.
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  2. #2
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    Quote Originally Posted by gammaman View Post
    How would I find complex intersections without the intersection function on the calculator.

    Say I have y=4xe^(-x^2) and y = |x|. How would I find this intersection.

    Note. I really only need the x values because I am trying to then find the area between these two curves.
    two cases ...

    (1) for x \geq 0

    4xe^{-x^2} = x

    4xe^{-x^2} - x = 0

    x(4e^{-x^2} - 1) = 0

    x = 0

    e^{-x^2} = \frac{1}{4}

    -x^2 = -\ln(4)

    since x > 0 ...

    x = \sqrt{\ln(4)}


    (2) for x < 0

    4xe^{-x^2} = -x

    4xe^{-x^2} + x = 0

    x(4e^{-x^2} + 1) = 0

    x = 0 only


    seems I've solved this before ... ?
    Last edited by mr fantastic; March 14th 2009 at 01:18 PM. Reason: No edit. Yes, you have. The OP apologised but the apology accidently got deleted in my re-structuring of this thread.
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  3. #3
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    Thanks. One more question. I have not had to find intersections in a long time. What if I had something simple like

    x^3 = 3x+2

    \Rightarrow x^3-3x-2=0

    seems I forgot how to find the roots when I have a power higher than 2.
    Last edited by mr fantastic; March 14th 2009 at 01:12 PM. Reason: Made the question clearer in light of later (now deleted) posts
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by gammaman View Post
    Thanks. One more question. I have not had to find intersections in a long time. What if I had something simple like

    x^3 = 3x+2

    \Rightarrow x^3-3x-2=0

    seems I forgot how to find the roots when I have a power higher than 2.
    Use general way of factorising by trial and error and if you fail

    Read This it can be helpful
    Last edited by mr fantastic; March 14th 2009 at 01:14 PM. Reason: Updated quote.
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  5. #5
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    Quote Originally Posted by gammaman View Post
    Thanks. One more question. I have not had to find intersections in a long time. What if I had something simple like

    x^3 = 3x+2

    \Rightarrow x^3-3x-2=0

    seems I forgot how to find the roots when I have a power higher than 2.
    The "rational root" theorem says that any rational number satisfying this equation must be an integer that divides 2. That tells you that the only possible rational roots are 1, -1, 2, and -2. Try those to see if there is a rational root.

    If not, then you will need to use "Ferrari's cubic formula" that ADARSH links to.
    Last edited by mr fantastic; March 14th 2009 at 01:15 PM. Reason: Updated quote
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