Question

lim x → infinity arctan(x^4 − x^6)

Answer 1

i tried the squeeze but still not sure what to do with -pi/2 < arctan(x^4(1-x^2) <pi/2

Answer 2

For large x, x^6 completely dominates over x^4 so the argumant of arctan will tend toward negative infinity. Therefore the limit you are seeking is -pi/2. http://fooplot.com/plot/oopgxdk0vi