# Thread: finding the limit with two variables

1. ## finding the limit with sandwich theorem

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

very confused...

2. Originally Posted by genlovesmusic09
$\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:
$u = n{y^{n - 1}},du = {n^2} - n({y^{n - 2)}}
$

$v = y + \frac{{{y^2}}}
{2},dv = 1 + y
$

$n{y^{n - 1}}(y + \frac{{{y^2}}}
{2}) - \int {y + \frac{{{y^2}}}
{2}(} {n^2} - n({y^{n - 2}}))
$