Posted by **Reen** on Sunday, October 18, 2009 at 9:48am.

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

any help is appreciated =D

- calculus - limits -
**Reiny**, Sunday, October 18, 2009 at 10:34am
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

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