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Math Help - finding the limit with two variables

  1. #1
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    finding the limit with sandwich theorem

    \lim n \to \infty \int_0^1 {\frac{{n{y^{n - 1}}}}<br />
{{1 + y}}} dy<br />

    very confused...
    Last edited by genlovesmusic09; December 6th 2009 at 05:56 PM.
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  2. #2
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    Quote Originally Posted by genlovesmusic09 View Post
    \lim n \to \infty \int_0^1 {\frac{{n{y^{n - 1}}}}<br />
{{1 + y}}} dy<br />

    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:
    u = n{y^{n - 1}},du = {n^2} - n({y^{n - 2)}}<br />
    v = y + \frac{{{y^2}}}<br />
{2},dv = 1 + y<br />
    n{y^{n - 1}}(y + \frac{{{y^2}}}<br />
{2}) - \int {y + \frac{{{y^2}}}<br />
{2}(} {n^2} - n({y^{n - 2}}))<br />
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