Which of These Statements Is True?
A) $\int_{0}^{\infty} t^{-4} e^{4 t} d t$

Multiple Choice

Which of these statements is true?

A) $\int_{0}^{\infty} t^{-4} e^{4 t} d t$ converges because $\frac{e^{4 t}}{t^{4}} \leq e^{4 t}$ , for all $t \geq 1$ and $\int_{0}^{\infty} e^{4 t} d t$ converges.
B) $\int_{0}^{\infty} t^{2} e^{-5 t} d t$ diverges because $t^{2} e^{-5 t} \geq t^{2}$ , for all $t \geq 1$ and $\int_{0}^{\infty} t^{2} d t$ converges.
C) $\int_{0}^{\infty} A^{4} e^{-2 t} d t$ converges because $t^{t} e^{-2 t}$ is of exponential order.
D) $\int_{0}^{\infty} t^{-4} e^{2 t} d t$ converges because $t^{-4} e^{2 t}$ is of exponential order.