Question

高数求极限，不知道怎么转化好

过程中试了几个x~sinx，还有x~arctanx都失败了

Answer 1

解：原式=lim(x->0)[(x-arctanx)/(x^2*arctanx)] (通分)
=lim(x->0)[(x/arctanx)*((x-arctanx)/x^3)]
=[lim(x->0)(x/arctanx)]*{lim(x->0)[(x-arctanx)/x^3]}
=1*{lim(x->0)[(x-arctanx)/x^3]}
=lim(x->0)[(x-arctanx)/x^3]
=lim(x->0)[(x-arctanx)'/(x^3)'] (0/0型极限，应用罗比达法则)
=lim(x->0)[(1/3)/(1+x^2)]
=(1/3)/(1+0)
=1/3。