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Math Help - help with limit

  1. #1
    Junior Member
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    help with limit

    hello,

    i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

    thus i need to evaluate the

    integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
    (x^2) e^[y(x^2)] dy dx

    = integral (from x=ln4 to x = infinity) of (e^x) - e dx

    = lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

    am i write?

    can someone evaluate the improper integral for me at a slow pace?

    Thanks very much!
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by pepsi View Post
    hello,

    i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

    thus i need to evaluate the

    integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
    (x^2) e^[y(x^2)] dy dx

    = integral (from x=ln4 to x = infinity) of (e^x) - e dx

    = lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

    am i write?

    can someone evaluate the improper integral for me at a slow pace?

    Thanks very much!
    your solution for integration is correct.

    but what do you mean by you asked to find the double limit of x^2e^{yx^2}

    see this is the area you want

    help with limit-zeft.jpg
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  3. #3
    Junior Member
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    Quote Originally Posted by Amer View Post
    but what do you mean by you asked to find the double limit of x^2e^{yx^2}


    Click image for larger version. 

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    i must be sleeping sorry it says the double integral of... i am learning double integrals

    p.s. it turns out i was wrong (having seen the answers at the back of the book. I should have known as well because the question asks for the bounded area so the answer is a finite number!

    Tx
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by pepsi View Post
    hello,

    i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

    thus i need to evaluate the

    integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
    (x^2) e^[y(x^2)] dy dx

    = integral (from x=ln4 to x = infinity) of (e^x) - e dx

    = lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

    am i write?

    can someone evaluate the improper integral for me at a slow pace?

    Thanks very much!
    it will be like this

    \int_{1}^{\ln 4} \int_{\frac{1}{x^2}}^{\frac{1}{x}} x^2 e^{y\cdot x^2 } dy dx

    this is the area after I do zoom to it the red area

    help with limit-zeft2.jpg
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