Question

evaluate as x approaches 0 (1-2cosx+cos^2(x))/x

Answer 1

0, use taylor's expansion series or L'hospital's principle

Answer 2

f(x) = 1-2cosx+cos^2(x))/x

differentiate top and bottom:

2sinx + 2cosxsinx = 2sinx(1 + cosx)

as x ---> 0 this approaches 0

Answer 3

yeah use L'hospital's rule, lim=f '(x)/g '(x)