Question

what's the limit of 3^x +2/e^2x +1 as x goes to infinity

Answer 1

you can throw away the +2 and +1, since they become insignificant.

Then you are left with just 3^x/e^(2x) = 3^x/(e^2)^x = (3/e^2)^x
since 3/e^2 < 1, the limit is zero