For each of the following improper integrals, carefully use the comparison test to decide if the integral converges or diverges. Give a reasonable "best" comparison function that you use in the comparison (by "best", we mean that the comparison function has known integral convergence properties, and is a reasonable upper or lower bound for the integrand we are evaluating).

1. $\int_{4}^{8}\,\displaystyle{5\over\sqrt{t-4}}\,dt$
This integral
A. converges
B. diverges

2. $\int_{-4}^{5}\,\displaystyle{dt\over(t + 4)^2}$
This integral
A. converges
B. diverges

3. $\int_{5}^{\infty} \displaystyle{d\theta\over\sqrt{\theta^3 + 2}}$
This integral
A. converges
B. diverges

4. $\int_{2}^{\infty} \displaystyle{dz\over e^z + 4^z}$
This integral
A. converges
B. diverges

5. $\int_{3}^{\infty} \displaystyle{5 + \sin z\over z}\,dz$
This integral
A. converges
B. diverges