Question

How do you evaluate the limit x->infinity of arctan(x-x^4)

Answer 1

Okay, my best try.

Inverse tan is an odd function that ranges between - pi/2 to pi /2

If the expression is x^2 for example, you use pi/2 since it will never be odd.

So what you have is:

limit as x approaches infinity of Inverse tangent of (- pi /2 - (pi/2)^4)

= -pi /2 - (pi)^4/16

can reduce a little which would be:

pi/2 * [ -1- (pi)^3/8]