lim(x→0)=（arctanx-x）/ln(1+2x^3)
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lim(x→0)=（arctanx-x）/ln(1+2x^3)lim(x→0)=（arctanx-x）/ln(1+2x^3)lim(x→0)=（arctanx-x）/ln(1+2x^3)说明：此题书写
lim(x→0)=（arctanx-x）/ln(1+2x^3)
lim(x→0)=（arctanx-x）/ln(1+2x^3)
lim(x→0)=（arctanx-x）/ln(1+2x^3)
说明：此题书写错误,应该是“lim(x→0)[(arctanx-x)/ln(1+2x^3)]”.
原式=lim(x->0)[(arctanx-x)'/(ln(1+2x^3))'] (0/0型极限,应用罗比达法则)
=lim(x->0)[-(1+2x^3)/(6(1+x^2))]
=-(1+0)/(6(1+0))
=-1/6.
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