lim(x趋向0)arctanx-sinx/x^3

来源：学生作业帮助网编辑：六六作业网时间：2024/12/20 11:57:40

lim(x趋向0)arctanx-sinx/x^3lim(x趋向0)arctanx-sinx/x^3lim(x趋向0)arctanx-sinx/x^3lim(x→0)(arctanx-sinx)/x&

lim(x趋向0)arctanx-sinx/x^3
lim(x趋向0)arctanx-sinx/x^3

lim(x趋向0)arctanx-sinx/x^3
lim(x→0) (arctanx - sinx)/x³,洛必达法则
= lim(x→0) [1/(1 + x²) - cosx]/(3x²)
= (1/3)lim(x→0) (1 - cosx - x²cosx)/(x² + x⁴),洛必达法则
= (1/3)(1/2)lim(x→0) (sinx - 2xcosx + x²sinx)/(x + 2x³),洛必达法则
= (1/6)lim(x→0) (- cosx + 4xsinx + x²cosx)/(1 + 6x²)
= (1/6)(- 1 + 0)/(1 + 0)
= - 1/6

lim(x→0-）（arctanx-sinx/x^3)
=lim(x→0-）arctanx-lim(x→0-）sinx/x^3
=0-∞
=-∞
lim(x→0+）（arctanx-sinx/x^3)
=lim(x→0+）arctanx-lim(x→0+）sinx/x^3
=0-∞
=-∞
故此式极限不存在

求lim x趋向于0(arctanx)/(x^+1) 求lim x趋向于0(arctanx)/(x^2+1) lim(x趋向0)(arctanx-x)/sinx^3 lim(x趋向0)arctanx-sinx/x^3 当x趋向于0+,lim arctanx/lnx=? lim(x趋向0)（x-arctanx）/（x-arcsinx）=? 当X趋向于0时证明lim arctanX/X=1 【求极限】(x趋向正无穷)lim((x^2)/arctanx). lim(arctanx/x)的极限x趋向无穷 Lim(arctanx/x)的值x趋向无穷大 lim x趋向于无穷（arctanx）/x lim(arctanx/2x) x趋向于零求lim(arcsinx·arctanx)/2x2的极限,x趋向于0 lim(x趋向0)ln(1+sin x)/x^2 lim(x趋向0) x^2 / (sin^2) * x/3 lim(x趋向0) x^2 / (sin^2) * x/3 lim (x趋向于0) sin(sinx)/x lim (x趋向于0)sin(sinx)/sinx