第1个回答 2010-04-06
因为 lim x→∞(1+1/x)^x=e将X用-X代替，那么-X→∞，可得lim x→∞(1-1/x)^-x=e,则lim x→∞(1-1/x)^x=[lim x→∞(1-1/x)^-x]^-1=e^-1即得证。 5.cosx *siny*cosz =[sin(x+y)-sin(x-y)]cosz/2(x+y+z=π/2)=[cosz-sin(x-y)]cosz/2(因x>=y)<=cos²z/2=(1+cos2z)/4（因z>=π/12）则cosx *siny*cosz<=(1+1/2)/4=3/8(当x=y=5π/24,z=π/12时取得）原式最大值=3/8cosx *siny*cosz=cosx[sin(y+z)-sin(z-y)]/2(x+y+z=π/2)=cosx[cosx+sin(y-z)]/2(因z<=y)>=cosx(cosx-0)/2=cos²x/2因z>=π/12，y>=π/12故z+y>=π/6则π/2-x>=π/6x<=π/3故cosx>=1/2则原式>=1/8(当z=y=π/12，x=π/3时取得）综上1/8<=cosx *siny*cosz <=3/8
得电阻为cosx-0)/2=cos²x/2因z>=π/12