求大神指教一道高数题

求大神指教一道高数题如图所示
2024-11-24 10:34:36
推荐回答(1个)
回答1:

原式=lim(x->0) ln[(sinx/x)^(1/x^2)]
=lim(x->0) ln{{(1+sinx/x-1)^[1/(sinx/x-1)]}^[(sinx/x-1)/x^2]}
=lim(x->0) ln{e^[(sinx/x-1)/x^2]}
=lim(x->0) (sinx-x)/x^3
=lim(x->0) (cosx-1)/3x^2
=lim(x->0) (-x^2/2)/3x^2
=-1/6