(cosx-e^((-x^2)/2))/(x^4)的极限x→0时

Question

(cosx-e^((-x^2)/2))/(x^4)的极限x→0时

Answer 1

原式=
lim{x->0}[1-x^2/2+x^4/24+o(x^4)-(1-x^2/2+x^4/8+o(x^4))]/[x^2(x-x+x^2/2+o(x^2)]
=lim{x->0}[-x^4/12+o(x^4)]/[x^4/2+o(x^4)]
=lim{x->0}[-/12+o(1)]/[1/2+o(1)]
=-1/6
因为分子是4阶无穷小,分母是高于3阶的无穷小,所以ln(1-x)至少要展开到平方项啦.
请采纳答案,支持我一下.