I have encountered a problem when applying the l'hopital rule to the following limit; could anyone help to see where i went wrong?
lim x->infinity (1+e^x+2e^2x) / (x+e^x+e^2x) ------(1);
repeating application of the rule gives:
lim x->infinity (e^x+4e^2x) / (1+e^x+4e^2x);
which then gives
lim x->infinity (e^x+8e^2x) / (e^x+8e^2x) = 1;
However in the solution provided, e^-2x is multiplied to (1), giving:
lim x->infinity (e^-2x+e^-x+2) / (xe^-2x+e^-x+1) = 2/1 = 2;
which is different from my answer.
Any help is much appreciated