已知函数f(x)=sin*2/x+更号3sin2/xcos2/x－2/1.
1个回答
(1)f(x)=sin^2(x/2)+√3sin(x/2)cos(x/2)-1/2
=(1/2)(1-cosx)+(√3/2)sinx-1/2
=(√3/2)sinx-(1/2)cosx
=sinxcos30°-cosxsin30°
=sin(x-30°)=sin(x-π/6）
由2kπ-π/2≤x-π/6≤2kπ+π/2得2kπ-π/3≤x≤2kπ+2π/3
[2kπ-π/3,2kπ+2π/3]是增区间
由2kπ+π/2≤x-π/6≤2kπ+3π/2得2kπ+2π/3≤x≤2kπ+5π/3
[2kπ+2π/3,2kπ+5π/3 ]是减区间
(2)y=g(x)=sinx=1/2得x1=π/6,x2=5π/6,x3=π/6+2π,x4=5π/6+2π
x5=π/6+4π,x6=5π/6+4π,看图形得x1+x2=π,x3+x4=π+4π,x5+x6=π+8π,.
数列{xn}的前2n项和=nπ+(n(n-1)/2)4π=2n*nπ+nπ
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