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Math Help - exponential question

  1. #1
    Senior Member mollymcf2009's Avatar
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    exponential question

    Can someone explain the difference between:

    e^{(x^2)} and e^{x^2}

    I'm sure it is a simple answer, but as my Calc II final is tomorrow, I'm practically brain dead
    Thanks!
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  2. #2
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    Talking

    Other than that e^{x^2} might be taken for (e^x)^2 when typed as text, I'm not sure there is a difference.
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by stapel View Post
    Other than that e^{x^2} might be taken for (e^x)^2 when typed as text, I'm not sure there is a difference.

    Their graphs are different, that is why I ask. Here is how I put them into my calculator:

    y = e^(x)^2 *this one looks like your run of the mill exponential compressed vertically

    y = e^(x^2) *this one looks like a vertically compressed parabola, vertex @ (0,1)

    I just need to know because I'm pretty sure I'll see it tomorrow on my final in the volumes of rotation section
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  4. #4
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    Quote Originally Posted by mollymcf2009 View Post
    Their graphs are different, that is why I ask. Here is how I put them into my calculator:

    y = e^(x)^2 *this one looks like your run of the mill exponential compressed vertically

    your calculator is interpreting this syntax as e^(2x)

    y = e^(x^2) *this one looks like a vertically compressed parabola, vertex @ (0,1)

    I just need to know because I'm pretty sure I'll see it tomorrow on my final in the volumes of rotation section
    .
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  5. #5
    Senior Member mollymcf2009's Avatar
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    Ok, this is the problem:

    Consider the region bounded by the curves:

    y = e^{x^2} ........ etc. etc.

    So, how do I interpret that? No parentheses anywhere. What does this graph look like?
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  6. #6
    Senior Member mollymcf2009's Avatar
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    I think I've got it

    Ok, So I'm assuming that since like Skeeter said e^{(x^2)} is being interpreted at e^{(2x)} that the graph of e^{x^2} looks like e^x but compressed vertically is the correct graph.
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  7. #7
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    Quote Originally Posted by mollymcf2009 View Post
    Ok, So I'm assuming that since like Skeeter said e^{(x^2)} is being interpreted at e^{(2x)} that the graph of e^{x^2} looks like e^x but compressed vertically is the correct graph.
    that's not what I said ... e^(x)^2 is interpreted as e^(2x) by the calculator, because the calculator sees the expression as the quantity (e^x) squared

    e^(x^2) is the correct calculator syntax for the desired even function, e^{x^2}.
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  8. #8
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by skeeter View Post
    that's not what I said ... e^(x)^2 is interpreted as e^(2x) by the calculator, because the calculator sees the expression as the quantity (e^x) squared

    e^(x^2) is the correct calculator syntax for the desired even function, e^{x^2}.
    Ok, sorry, I guess I just read it wrong. Thanks for clarifying! So the graph DOES look like a compressed parabola. Glad you caught me on that!
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  9. #9
    MHF Contributor Calculus26's Avatar
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    Molly

    Good Luck on your Final tommorow
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