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sin2x乘sin3x

lim(x到0)[(sin2x /2x)*2x]/[(sin3x/3x)*3x]=2/3备注:sin2x/2x=1 ,sin3x/3x=1就是sinx/x的应用呀请指教

洛必达法则 上下求导2cos2x/3cos3x,cos0=1 结果2/3

=∫sin2x(sin2xcosx+cos2xsinx)dx =∫sin2xsin2xcosx+sin2xcos2xsinx dx =1/2∫(1-cos4x)cosx+sin4xsinx dx 拆开,用cos二倍角公式 =1/2∫cosx-cos5x dx =1/2∫cosx dx-1/2∫cos5x1/5(5x)`dx =1/2sinx-1/10∫cos5x d5x =1/2sinx-1/10sin5x

∫ sinxsin2xsin3x dx积化和差=(1/2)∫ (cosx - cos3x)sin3xdx=(1/2)∫ (cosxsin3x - cos3xsin3x)dx积化和差=(1/4)∫ (sin4x + sin2x - sin6x)dx=-(1/16)cos4x - (1/8)cos2x + (1/24)cos6x + C希望可以帮到你,如果解

是不是:limx趋近于0 sin3x/sin2x=sin3x/3x/sin2x/2x*3x/2x=1/1*3/2=3/2=1.5

分子分母都趋近0,求导就行 lim(sin2x/sin3x) =lim(xsin2x/xsin3x) =lim2/3(3xsin2x/2xsin3x) =lim2/3(sin2x/2x)/(sin3x/3x) =2/3lim(sin2x/2x)/lim(sin3x/3x) =2/3

2π 解:sin(2x)的最小正周期是:2π/2=π sin(3x)的最小正周期是:2π/3 ∵2π/π=2,2π/(2π/3)=3,2与3互质 ∴sin2x + sin3x的最小正周期是2π PS:1,附上y=sin2x + sin3x的图像,以供验证2,1和2/3的广义最小公倍数是2

y=sin3x ln(sin2x) y'=3cos3x ln(sin2x)+sin3x /sin2x *2cos2x=3cos3xln(sin2x)+2sin3xcot2x

sin2x*sin2x=sin2x=(1-cos4x)/2

sin2x=2sinxcosx,sin3x=3sinx-4(sinx)^3,依题意2sinxcosx=sinx[3-4(sinx)^2]①,由①式可得sinx=0②或2cosx=3-4(sinx)^2,即4(cosx)^2-2cosx-1=0③;由②得x=kπ;由③得cosx=(1±√5)/4,x=π/5+2kπ、x=3π/5+2kπ;综上所述,原三角方程的解为x1=kπ、x2=(10k+1)π/5、x3=(10k+3)π/5,k=0、±1、±2、为整数.

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