Question

lim(t to ∞)[(t^2)/e^t]

Answer 1

\[\lim_{t\to\infty}(t^2)/e^t = \infty/\infty\] which permits you to use l'hopital's rule
\[\lim_{t\to\infty}(2t)/e^t = \infty/\infty\] which permits u to use l'hopital's rule, again so;
\[\lim_{t\to\infty}(2)/e^t = 0\] finally an answer.

Answer 2

t^2/e^t
t^2
=--------
1+t+t^2/2!+.....
1
=--------
t^-2 +t^-1+1/2!+t/3!......

1
=-----------
0+0+0.5+t/6+.....

=0 when t->infty