lim(x→0)(sinx/x)^(1/1-cosx)等于

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lim(x→0)(sinx/x)^(1/1-cosx)等于

lim(x→0)(sinx/x)^(1/1-cosx)等于
lim(x→0)(sinx/x)^(1/1-cosx)等于

lim(x→0)(sinx/x)^(1/1-cosx)等于
=e^ lim (1/1-cosx)·ln(sinx/x)
=e^ lim ln(sinx/x)/(1-cosx)
=e^ lim (sinx/x -1)/(x²/2)
=e^ lim 2(sinx-x)/x³
=e^ lim 2(cosx-1)/(3x²)
=e^ lim 2(-x²/2)/(3x²)
=e^(-4/3)

1-cosx约等于1/2x平方