Question

Lim (x-pi/2)sin(pi/x) as x goes to +infinity?

Answer 1

Use `lim_(trarr0)sint/t = 1` and `lim_(xrarroo)pi/x = 0`

Explanation:

`(x-pi/2)sin(pi/x) = pi/x(x-pi/2) sin(pi/x)/(pi/x)`

`= (pi-pi^2/(2x))sin(pi/x)/(pi/x)`

Limit at `oo` is `(pi-0)(1) = pi`