洛必达法则 limx趋近于0 tanx-sinx/x^3？

求lim(x趋于0) (tanx-sinx)/x^3

原式为0/0型,运用洛必达法则得lim(x趋于0) (tanx-sinx)/x^3=lim(x趋于0) (sec^2x-cosx)/3x^2=lim(x趋于0) (1-cos^3x)/3x^2=lim(x趋于0) (3cos^2xsinx)/6x=1/2

求极限:lim(x→0)(tanx-sinx)/x^3

lim(x→0)[(tanx-sinx)/(sinx)^3] =lim(x→0)[(sinx/cosx-sinx)/(sinx)^3] =lim(x→0)[(1/cosx-1)/(sinx)^2] =lim(x→0){(1-cosx)/[cosx(sinx)^2]} =lim(x→0)(1/cosx)(1-cosx)/[1-(cosx)^2] =lim(x→0)(1/cosx)(1-cosx)/[(1+cosx)(1-cosx)] =lim(x→0)(1/cosx)[1/(1+cosx)] =1*[1/(1+1)] =1/2.

limx->0 (tanx-sinx)/x^3 怎么求?

limx->0 (tanx-sinx)/x^3 =limx->0 (sinx-sinx*cosx)/cosx*x^3=limx->0 (sinx-sinx*cosx)/x^3=limx->0 (sinx-(sin2x)/2)/x^3展开:sinx=x-x^3/3!+o,sin2x=2x-(2x)^3/3!+o(之所以只要展到3次方项是因为分母最高项是3)原式=limx->0(-x^3/6 + 8 x^3/12)/x^3 =1/2

limxsinx x趋近于0

sinx x趋于无穷大

limsinx x趋于0

limx 0tanx-sinx除以x3

limsinx x趋于无穷

limi0 tanxsinx 3 x

limsinx趋近于x0时

limx 0tanx的sinx次方

limx趋于0(tanx-sin)/x^3用洛比达法则

原式=lim(x-->0)[(sinx/cosx-sinx)/sin(x^3)] =lim(x-->0)(sinx/cosx)(1-cosx)/sin(x^3)] =lim(x-->0)[(x/cosx)(x^2/2)/x^3] =lim(x-->0)[(x^3/2cosx)/x^3] =lim(x-->0)[1/2cosx]=1/2

lim(x-0)[(tanx-sinx)/x^3]=lim(tanx/x^3)-lim(sinx/x^3)=lim(x/x^3)-lim(x/x^3).

解:这里如果只是lim(tanx/x^3)-lim(sinx/x^3)=lim(x/x^3)-lim(x/x^3)=0这个是没有错的,但是你前面还有式子lim(x-0)[(tanx-sinx)/x^3],因为(tanx-sinx)/x^3,当x趋于0是,分.

lim(x→0) tanx-sinx/x3方 用洛必达法则解答 :

lim(x→0) (tanx-sinx) / x³= lim(x→0) tanx (1 - cosx) / x³ 先用等价无穷小代换 tanx ~ x= lim(x→0) (1 - cosx) / x²= lim(x→0) sinx / (2x) 洛必达法则 = 1/2

求极限x趋向于0,limtanx-sinx/x^3 为什么这样做不对

不是极限,是等价无穷小当x趋向于0, x-sinx ~ x^3/6

求limx趋近于0tanx-sinx/x三次方

lim x趋近于0 (tanx-sinx)/x的三次方=lim x趋近于0 tanx(1-cosx)/x的三次方=lim x趋近于0 x(x方/2)/x的三次方=lim x趋近于0 (x的3次方/2)/x的三次方=1/2

lim(x趋向于0)(tanx-sinx)/x^3=?

lim(x→0)(tanx-sinx)/x^3=lim(x→0)(sinx/cosx-sinx)/x^3=lim(x→0)(1-cosx)/x^2=lim(x→0)1/2x^2/x^2=1/2

求极限lim. tanx-sinx / x^3

tanx-sinx / x^3 =[sinx(1-cosx)]/(x^3*cosx) =(sinx/x)*(1-cosx)/x^2 (当x趋于0时,cosx的极限是1) =1*1/2 (1-cosx与1/2 * x^2等价,当x趋于0时)( sinx/x极限是1)=1/2