盐城2011高三数学调研已知函数设f(x)=1+x-(x^2)/2+(x^3)/3-(x^4)/4+.+(x^2011)/2011已知函数f(x)=1+x-(x^2)/2+(x^3)/3-(x^4)/4+.+(x^2011)/2011,g(x)=1-x+(x^2)/2-(x^3)/3+(x^4)/4-.-(x^2011)/2011,设F(x)=f(x+3)*g(x-3),且函数F(x)的零点均

　　盐城2011高三数学调研已知函数设f(x)=1+x-(x^2)/2+(x^3)/3-(x^4)/4+.+(x^2011)/2011

　　已知函数f(x)=1+x-(x^2)/2+(x^3)/3-(x^4)/4+.+(x^2011)/2011,g(x)=1-x+(x^2)/2-(x^3)/3+(x^4)/4-.-(x^2011)/2011,设F(x)=f(x+3)*g(x-3),且函数F(x)的零点均在区间[a,b](a