大一高数题,求第5题详答,

1个回答

  • (2)lim(1-cosx)/x^2=lim(2(sin(x/2))^2)/x^2=lim(2(sin(x/2))^2)/x^2

    =lim(2*(x/2)^2)/x^2=1/2(等价无穷小 sin x/2=x/2)

    (5)洛毕塔法则

    =lim(e^x-cosx*e^x)/(1-cosx)

    =lim(e^x-cosx*e^x+sinx*e^x)/(sin x)

    =lim(e^x-cosx*e^x+2sinx*e^x+cosx*e^x)/(cosx)

    =lim(e^x+2sinx*e^x)/(cosx) (代入x=0)

    =1