limx趋于∞[(x∧2+x)arctanx]/[x∧3-x-3],求它的极限,

Question

lim x趋于∞ [(x∧2+x)arctanx]/[x∧3-x-3],求它的极限,

Answer 1

lim[(x∧2+x)arctanx]/[x∧3-x-3]
=lim(x∧2+x)/[x∧3-x-3]*lim(arctanx)
=0*(正负派/2)
=0
其中lim(x∧2+x)/[x∧3-x-3]=0,因为分子次数比分母低