# Limit diverges or converges

1. Sep 21, 2008

### graycolor

integral 2/(x-6)^2 respects to x from 0 to 8. Shouldn't the answer to this be converges and is =-4/3. The true answer to this is it diverges towards infinity... can someone please explain.

2. Sep 21, 2008

Two things to consider:

1. isn't there a number between $$0$$ and $$8$$ that could cause a problem?

2. The integrand $$2/{(x-6)^2}$$ is positive throughout the interval of integration,
so how could the integral be negative?

3. Sep 21, 2008

### graycolor

I think I've found the problem there should be an asymptote when x=6. My teacher never taught me to look for these.

4. Sep 21, 2008