Find lim x→∞ 1/(xe^-x) and show the work leading to your answer

Find the following limit:
lim_(x->∞) e^x/x

 

Since e^x grows asymptotically faster than the polynomial x as x approaches ∞, lim_(x->∞) e^x/x = ±∞.
Additionally e^x>0 and x>0 as x approaches ∞, so lim_(x->∞) e^x/x = ∞:
Answer: |∞