1. ## comparison test

i think this function will diverge but i dont what g should equal.
use comparsion test to show if function from 1 to infinitie x/(square root 1+ x^6) diverges or converges.

2. Originally Posted by twilightstr
i think this function will diverge but i dont what g should equal.
use comparsion test to show if function from 1 to infinitie x/(square root 1+ x^6) diverges or converges.
$\frac{x}{\sqrt{1 + x^6}} < \frac{x}{\sqrt{x^6}} = \frac{x}{x^3} = \frac{1}{x^2}$.

So the series is convergent by the comparison test.

3. can g be 1/x if not, why not

4. Originally Posted by twilightstr
can g be 1/x if not, why not
No. Because the series is convergent.

Re-read my first post. I have corrected my inequality.