lim(cosx)^(1/(1-cosx)).x趋向于0

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/25 14:42:38

原式=lim(x->0){[1+(cosx-1)]^[(1/(cosx-1))(-1)]}
=1/lim(x->0){[1+(cosx-1)]^(1/(cosx-1))}
=1/lim(t->0)[(1+t)^(1/t)] (令t=cosx-1)
=1/e (应用重要极限).

大数lim(cosx)^(1/(1-cosx)).x趋向于0 lim(cosx)^(1/(1-cosx)).x趋向于0 lim（x趋向于0）（1-cosx)/x^2 1-√cosx/xsinx 求Lim X趋向于0 lim极限趋向于0+求x/√(1-cosx) lim(x趋向于0)(cosx)^[1/(xsinx)]= lim(1-cosx)/x2 x趋向于0 lim X趋向于0 (cosX-1)/sinX lim(1-cosx)x趋向0, X趋向0 lim(xsinx)/(1-cosx) lim(1-cosx)/5x x趋向0 x趋向于0,lim[x*ln(1+3x)]/(1-cosx)