Answer: E) None of the above
Choice A comes close saying that [tex]\displaystyle \int_{1}^{\infty}\frac{1}{\sqrt{x}}dx[/tex] does diverge, which is true. But that doesn't conclusively say if the original integral converges or diverges. We don't have enough info. If 1/sqrt(x) converged, then we could say definitively that the original integral converged as well.
