If we try to evaluate this expression, we arrive at an indeterminate limit of the form ∞ · 0. So we rewrite this limit as
lim of [ e^(-x/5) / (1 / x^3) ] as x→∞
This results in an determinate form of 0/0, so we apply L'Hospital's rule by differentiating the numerator and denominator.
lim of [ -1/5e^(-x/5) / (-3/x^4) ] as x→∞
Multiply the numerator and denominator by x^4
lim of [ -1/5 * x^4 * e^(-x/5) / (-3) ] as x→∞
Since e^(-x/5) approaches 0 as x→∞, the limit evaluates to 0.
The answer to this question is 0.