Limits/Calculus?

Question

how do you do the limit as x approaches infinity of arctan (x^5-x^-7)? Thanks

Answer 1

x^5 - x^(-7) approaches infinity as x approaches infinity. You're basically looking for the arctan(infinity). In other words, the tangent of what is infinity. pi/2.

Keep in mind that the answer can be (2n+1)*pi/2. But it's often accepted that arctan(x) has a range of -pi/2 to pi/2.

Answer 2

1/(tan^-1(x)^2)