According to Maple, the series expansion of about is (EDIT: You can derive it by starting with the Taylor series for centered at and using long division.)
Since we're integrating over values close to 1, is approximately .
so
Last edited by Random Variable; Jun 2nd 2010 at 01:46 PM.
According to Maple, the series expansion of about is (EDIT: You can derive it by starting with the Taylor series for centered at and using long division.)
Since we're integrating over values close to 1, is approximately .
It is fairly easy to verify that for we have that and so . It follows that . Note though that the LHS is just and . The conclusion follows from the Squeeze Theorem.