Calculus: Early Transcendentals, Chapter 4, 4.4, Section 4.4, Problem 24

You need to evaluate the limit, hence, you need to replace oo for u:
lim_(u->oo) (e^(u/10))/(u^3) = (e^oo)/(oo) = oo/oo
Since the limit is indeterminate oo/oo , you may apply l'Hospital's rule:
lim_(u->oo) (e^(u/10))/(u^3) = lim_(u->oo) ((e^(u/10))')/((u^3)')
lim_(u->oo) ((e^(u/10))')/((u^3)') = lim_(u->oo) ((1/10)*e^(u/10))/(3u^2) = oo/oo
You need to use again l'Hospital's rule:
lim_(u->oo) ((1/10)*e^(u/10))/((3u^2)) = lim_(u->oo) ((1/100)*e^(u/10))/(6u) = oo/oo
You need to use again l'Hospital's rule:
lim_(u->oo) ((1/1000)*e^(u/10))/6 = 1/6000*e^oo = oo
Hence, evaluating the given limit using l'Hospital's rule, yields lim_(u->oo) (e^(u/10))/(u^3) = oo.