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.
limit tan^(-1) (x^2 - x^4) as x ---> ∞
set your calculator to radians
enter a huge number, multiply it by -1, then enter
I got -1.570796 or - pi/2
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