• Australopithecus
Apply the Comparison Test to determine if the integral converges or diverges. The Integral is $\int\limits_{0}^{1} e^{2x}dx/x^{3}$ So far I have that $\int\limits_{0}^{1} e^{2x}dx/x^{3} = \lim_{t \rightarrow 0^{+}} \int\limits_{t}^{1} e^{2x}dx/x^{3}$ Since $1/0^{+} = \infty$ I assume this integral is Divergent Therefore, I use f(x) < g(x) where f(x) = e^(2x)/x^(3) $e^{2x}/x^{3} \le 1/x^{3}$ Since $\lim_{t \rightarrow 0^{+}} \int\limits_{t}^{1} dx/x^{3}$ is Divergent by the C.T. $\int\limits_{0}^{1} e^{2x}dx/x^{3}$ is Divergent
Mathematics

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