作业帮设向量a=(cos(x/2),sin(x/2)),向量b=(sin(3x/2),cos(3x/2)),x∈[0,π/2].(1)求a·b及|a+b|;(2)若函数f(x)=a·b+(√2)|a+b|,求f(x)的最小值,最大值.
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![设向量a=(cos(x/2),sin(x/2)),向量b=(sin(3x/2),cos(3x/2)),x∈[0,π/2].(1)求a·b及|a+b|;(2)若函数f(x)=a·b+(√2)|a+b|,求f(x)的最小值,最大值.](/uploads/image/z/3913520-32-0.jpg?t=%E8%AE%BE%E5%90%91%E9%87%8Fa%3D%28cos%28x%2F2%29%2Csin%28x%2F2%29%29%2C%E5%90%91%E9%87%8Fb%3D%28sin%283x%2F2%29%2Ccos%283x%2F2%29%29%2Cx%E2%88%88%5B0%2C%CF%80%2F2%5D.%281%29%E6%B1%82a%C2%B7b%E5%8F%8A%7Ca%2Bb%7C%3B%282%29%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%3Da%C2%B7b%2B%28%E2%88%9A2%29%7Ca%2Bb%7C%2C%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%2C%E6%9C%80%E5%A4%A7%E5%80%BC.)
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设向量a=(cos(x/2),sin(x/2)),向量b=(sin(3x/2),cos(3x/2)),x∈[0,π/2].(1)求a·b及|a+b|;(2)若函数f(x)=a·b+(√2)|a+b|,求f(x)的最小值,最大值.
设向量a=(cos(x/2),sin(x/2)),向量b=(sin(3x/2),cos(3x/2)),x∈[0,π/2].
(1)求a·b及|a+b|;
(2)若函数f(x)=a·b+(√2)|a+b|,求f(x)的最小值,最大值.
设向量a=(cos(x/2),sin(x/2)),向量b=(sin(3x/2),cos(3x/2)),x∈[0,π/2].(1)求a·b及|a+b|;(2)若函数f(x)=a·b+(√2)|a+b|,求f(x)的最小值,最大值.
(1)a*b=sin(3x/2+x/2)=sin2x,|a+b|=根号(2+2sin2x) (2)f(x)=sin2x+2根号(1+sin2x),设t=根号(1+sin2x),因为x属于[0,派/2],所以t的范围是[0,根号2],sin2x=t^2-1,f(x)=t^2-1+2t=(t+1)^2-2,范围是[-1,1+2根号2]