Find the limit of

Question

(2cosx+3cosx-2)/(2cosx-1)as x tends to pi/3.

Answer 1

if you let y=cosx, then you have

(2u-1)(u+2)/(2u-1)

so, except when u=1/2, you just have (u+2)

so, the limit is cos pi/3 + 2 = 5/2

there is a removable hole at x=pi/3