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Thread: finding the limit with two variables

  1. #1
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    finding the limit with sandwich theorem

    $\displaystyle \lim n \to \infty \int_0^1 {\frac{{n{y^{n - 1}}}}
    {{1 + y}}} dy
    $

    very confused...
    Last edited by genlovesmusic09; Dec 6th 2009 at 04:56 PM.
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  2. #2
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    Quote Originally Posted by genlovesmusic09 View Post
    $\displaystyle \lim n \to \infty \int_0^1 {\frac{{n{y^{n - 1}}}}
    {{1 + y}}} dy
    $

    very confused...
    I figured out I am supposed to use integration by parts and that the integral from that is too complicated and you use the sandwich/pinching/squeeze theorem
    this is what i got for integration by parts:
    $\displaystyle u = n{y^{n - 1}},du = {n^2} - n({y^{n - 2)}}
    $
    $\displaystyle v = y + \frac{{{y^2}}}
    {2},dv = 1 + y
    $
    $\displaystyle n{y^{n - 1}}(y + \frac{{{y^2}}}
    {2}) - \int {y + \frac{{{y^2}}}
    {2}(} {n^2} - n({y^{n - 2}}))
    $
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