limit as x approaches infinity; tan^(-1) (x^2 - x^4)

Question

any help is appreciated =D

Answer 1

I am going to use an intuitive approach

let theta = tan^-1 (x^2 - x^4)

or tan(theta) = x^2 - x^4
now as x---> ∞ the right side of the above equation ---> - ∞

I know that tan 90º or tan(pi/2) is undefined, but as I approach 90º or pi/2
the tangent value becomes infinitely large positively,
and the tangent of -90º or -pi/2 becomes -infinitely large.

so
limit tan^(-1) (x^2 - x^4) as x ---> ∞
= -pi/2

check:
set your calculator to radians
enter a huge number, multiply it by -1, then enter
2nd Tan
I got -1.570796 or - pi/2