那我就不用洛必达法则了呵呵~,用定理lim[x→0] sinx/x=1
lim[x→0] (tanx-sinx)/x³
=lim[x→0] (sinx/cosx-sinx)/x³
=lim[x→0] (sinx-sinxcosx)/(x³cosx)
=lim[x→0] sinx(1-cosx)/(x³cosx)
=lim[x→0] sin³x(1-cosx)/(x³sin²xcosx)
=lim[x→0] (sinx/x)³·(1-cosx)/(sin²xcosx)
=lim[x→0] (sinx/x)³·(1-cosx)/[(1-cos²x)cosx]
=lim[x→0] (sinx/x)³·(1-cosx)/[(1+cosx)(1-cosx)cosx]
=lim[x→0] (sinx/x)³·1/[(1+cosx)cosx]
=1·1/(1+1)
=1/2
求极限:lim(x→0)(tanx-sinx)/x^3
求极限:lim(x→0)(tanx-sinx)/x^3
数学人气:473 ℃时间:2019-09-01 11:30:44
优质解答
我来回答
类似推荐
猜你喜欢
- 1it seems that的用法
- 2小明以每秒两米的速度沿铁路旁的人行道跑步,身后开来一辆长188米的火车,火车每秒行18米,
- 3若x的2m-n次方=2,x的2m+n次方=1,求(x的四次方)方之m-(x²)的n次方的值
- 4She wants to c___the color
- 5英语翻译
- 6The teacher with a number of students of students___in the classroom
- 7英语翻译
- 8writing to my I'm an e-mail English friend(.)连词成句
- 9求多项式7x^3-6x^3y+3x^2y+3x^3+6x^3y-3x^2y-10x^3+10,x=12/13,小马虎说这道题没有给出y的值
- 10All parents love their children and my parents love ______ too