Limit trouble

1. The problem statement, all variables and given/known data
a.\lim_x -->infty arctan(x^2-x^4) =
b.\lim _x --->pi/2 e^tan (x) =

2. Relevant equations
Limit laws


3. The attempt at a solution

a. I know I can use the limit laws to take the limit of Arctan@infinity=1/2, but then, I don't know if I should factor out the (x^2-x^4)

b. Don't even know.

 

Ok, Im pretty sure b. is 0 because of the rule lim x-->infin e^X=0. We can substitute and look at the graph and it is 0.

Still not sure about a., taking the limit of Arctan@infinity=1/2 and (x^2-x^4) approaches -infinity so what then?

 

I am looking as it approaches +infinity(sorry if I didn't specify) and I am positive it is 1/2. Basicaly [lim x->inf. arctan=1/2]*[lim x->inf. (x^2-X^4)=+infinity}
right?