已知函数f(x)=sin^2(x/2+派/12)+根号3sin(x/2+派/12)cos(x/2+派/12)-1/2.(1)求f(x)的值域.(2)若f(x)(x>0)的图像与直线y=1/2交点的横坐标由大到小依此是x1,x2,…,xn,求数列{xn}的前2n项的和.
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![已知函数f(x)=sin^2(x/2+派/12)+根号3sin(x/2+派/12)cos(x/2+派/12)-1/2.(1)求f(x)的值域.(2)若f(x)(x>0)的图像与直线y=1/2交点的横坐标由大到小依此是x1,x2,…,xn,求数列{xn}的前2n项的和.](/uploads/image/z/1748829-21-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%5E2%28x%2F2%2B%E6%B4%BE%2F12%29%2B%E6%A0%B9%E5%8F%B73sin%28x%2F2%2B%E6%B4%BE%2F12%29cos%28x%2F2%2B%E6%B4%BE%2F12%29-1%2F2.%EF%BC%881%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F.%EF%BC%882%EF%BC%89%E8%8B%A5f%28x%29%28x%3E0%29%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D1%2F2%E4%BA%A4%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E7%94%B1%E5%A4%A7%E5%88%B0%E5%B0%8F%E4%BE%9D%E6%AD%A4%E6%98%AFx1%2Cx2%2C%E2%80%A6%2Cxn%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bxn%7D%E7%9A%84%E5%89%8D2n%E9%A1%B9%E7%9A%84%E5%92%8C.)
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已知函数f(x)=sin^2(x/2+派/12)+根号3sin(x/2+派/12)cos(x/2+派/12)-1/2.(1)求f(x)的值域.(2)若f(x)(x>0)的图像与直线y=1/2交点的横坐标由大到小依此是x1,x2,…,xn,求数列{xn}的前2n项的和.
已知函数f(x)=sin^2(x/2+派/12)+根号3sin(x/2+派/12)cos(x/2+派/12)-1/2.(1)求f(x)的值域.(2)若f(x)(x>0)的图像与直线y=1/2交点的横坐标由大到小依此是x1,x2,…,xn,求数列{xn}的前2n项的和.
已知函数f(x)=sin^2(x/2+派/12)+根号3sin(x/2+派/12)cos(x/2+派/12)-1/2.(1)求f(x)的值域.(2)若f(x)(x>0)的图像与直线y=1/2交点的横坐标由大到小依此是x1,x2,…,xn,求数列{xn}的前2n项的和.
f(x)=sin^2(x/2+π/12)+√3sin(x/2+π/12)cos(x/2+π/12)-1/2
=(1/2)[1-cos(x+π/6)]+(√3/2)sin(x+π/6)-1/2
=sinx,
(1)f(x)的值域是[-1,1].
(2)x1=π/6,x2=5π/6,
x=(2k-2+1/6)π,x=(2k-2+5/6)π,k∈N+,
数列{xn}的前2n项的和
=n(x1+x2)+(1/2)n(n-1)*4π
=nπ+2n(n-1)π
=(2n^2-n)π.