Question

limx→∞ e^x/x². solve using L- Hospital rule

Answer 1

Answer:

Consider r>0; then

limx→∞xrex=0

Indeed, you can start from x<ex (for x>0), so x2<ex/2 and therefore

0<xex<2ex/2

and the squeeze theorem allows to conclude. Of course also l’Hôpital works:

limx→∞xex=limx→∞1ex

For the general limit, write it as

limx→∞(xex/r)r=limx→∞rr(x/rex/r)r=0