Improper Integral: Comparing to 1/x^p

[cragar]

Homework Statement

integral from 2 to infinty 1/(x-sqrt(x))

The Attempt at a Solution

my teacher wants us to compare it to another function in the form 1/x^p
and not integrate it so
would i compare it to 1/x and then do the limit comparison test
limit as x approaches infinity
i came out with a finite number and since 1/x divegres therefore 1/(x-sqrt(x)) diverges
is this correct.

 

[tiny-tim]

integral from 2 to infinty 1/(x-sqrt(x))
…
my teacher wants us to compare it to another function in the form 1/x^p
and not integrate it so
would i compare it to 1/x and then do the limit comparison test
limit as x approaches infinity

Hi cragar!

That'll do, but you don't actually need the limit comparison test in this case, since 1/(x - √x) is always larger than 1/x

 

[cragar]

so you are saying since it is larger than something that diverges then it to will diverge.
i see.