(Ⅰ)若曲线c1:y=f(x)与曲线c2:y=g(x)存在公切线,求a最大值.
(Ⅱ)当a=1时,F(x)=f(x)﹣bg(x)﹣cx﹣1,且F(2)=0,若F(x)在(0,2)内有零点,求实数b的取值范围.