How would I find the limit of 9+17arctan(n!)/(3^n)?

Answer 1

arctan will return a value between -pi/2 and pi/2. Because it is bound, the limit of it divided by 3^n as n approaches infinity is 0.

Thus, lim (n -> oo) 9+17arctan(n!)/(3^n) = 9

Answer 2

n!/3^n increases without bound as n -> infinity.

arctan(n!/3^n) approaches pi/2 (radians) or 180 degrees as n!/3^n approaches infinity.

So the limit will be 9+17(pi/2) or approximately 35.7