Advocates of limited government are not anti-government per se, as some people would charge. Rather, they are hostile to concentrations of coercive power and to the arbitrary use of power against right. With a deep appreciation for the lessons of history, and the dangers of unconstrained government, they are for constitutionally limited government, with the delegated authority and means to protect our rights, but not so powerful as to destroy or negate them.
Libertarians agree that freewill and determinism are incompatible, but believe that determinism is false and we have freewill. In other words: we have free will, therefore determinism must be false. (See the works from Holbach on this aspect - althuig I do mostly not agree with him, he has some excellent points.)