7.3.16.
We make the substitution x = 1 sec , keeping in mind that 0 < or
3
2
< 32 . Then dx = 1 sec tan d. To change the bounds, we make use of
3
the fact that sec = (cos )1 . For x = 2 we have
3
2
1
= sec
3
3
1
2=
cos
1
cos =
2
and 0 < implies = . Sim
11.3.32
Using the integral test, we will find out that:
()
(
(
(
)
( )
)
(
)
So the condition for the series to be convergent is p > 1
11.4.20
Using the comparison test we know that:
First series on the right hand side of the above inequality is a converg