Answer
for $1{\leq}x{\lt}\infty$
$\frac{e^{-x}}{x}$ $\lt$ $\frac{1}{x}$
but $\int_1^{\infty}{\frac{dx}{x}}$ diverges. An intergral is smaller than a divergent intergral does not allow to draw any conclusion using the comparison test
Work Step by Step
for $1{\leq}x{\lt}\infty$
$\frac{e^{-x}}{x}$ $\lt$ $\frac{1}{x}$
but $\int_1^{\infty}{\frac{dx}{x}}$ diverges. An intergral is smaller than a divergent intergral does not allow to draw any conclusion using the comparison test
