Verified answer

lim = 1 , as x-> ∞

Well lets think about it.

e^-3x is the same thing as 1/e^3x

1/e^3x is gonna go to 0 when we take the limit.

So we will be left with whatever:

e^3x / e^3x does

And those are the same terms divided by each other so itll be 1.

(e^(3x) - e^(-3x)) / (e^(3x) + e^(-3x)) =>

((e^(6x) - 1) / e^(3x)) / ((e^(6x) + 1) / e^(3x)) =>

(e^(6x) - 1) / (e^(6x) + 1) =>

(e^(6x) + 1 - 2) / (e^(6x) + 1) =>

(e^(6x) + 1) / (e^(6x) + 1) - 2 / (e^(6x) + 1) =>

1 - 2 / (1 + e^(6x))

x goes to infinity

1 - 2 / (1 + e^(6 * inf)) =>

1 - 2 / (1 + e^(inf)) =>

1 - 2 / (1 + inf) =>

1 - 2 / (inf) =>

1 - 0 =>

1