=lim(x^2-sin^2x)/x^4
=lim(2x-2sinxcosx)/4x^3
=lim(2x-sin2x)/4x^3
=lim(2-2cos2x)/12x^2
=lim4sin2x/24x
=4/12=1/3
1\/sin^2x-1\/x^2 x趋向0求极限
lim(1\/sin^2x-1\/x^2)=lim(x^2-sin^2x)\/x^4 =lim(2x-2sinxcosx)\/4x^3 =lim(2x-sin2x)\/4x^3 =lim(2-2cos2x)\/12x^2 =lim4sin2x\/24x =4\/12=1\/3
1\/sin^2x-1\/x^2 x趋向0求极限
lim(1\/sin^2x-1\/x^2)=lim(x^2-sin^2x)\/x^4 =lim(2x-2sinxcosx)\/4x^3 =lim(2x-sin2x)\/4x^3 =lim(2-2cos2x)\/12x^2 =lim4sin2x\/24x =4\/12=1\/3
求极限:lim(1\/sin^2(x)-1\/x^2),x->0
(sinx+x)*x\/sin^2(x)当x->0时极限是2 下面只要求(-sinx+x)\/x^3的极限 可以用洛比达法则 lim(-sinx+x)\/x^3=lim(-cosx+1)\/3x^2=sinx\/6x=1\/6 所以整个极限是2\/6=1\/3
当x趋近于0时,求(1\/sin^2x)-1\/x^2的极限
x^2*sin^2x等价于x^4 所以原极限=lim(x趋于0) 2x *(x -sinx) \/ x^4 =lim(x趋于0) 2(x -sinx) \/ x^3 所以洛必达法则求导 =lim(x趋于0) 2(1 -cosx) \/ 3x^2 而1-cosx等价于0.5x^2，代入得到原极限= 2* 0.5x^2 \/3x^2= 1\/3 ...
(1\/(sinx)^2-1\/(x^2))当X趋于0时的极限是多少最好有过程?非常感谢...
x->0 lim[1\/(sinx)^2-1\/x^2]=lim[(x^2-(sinx)^2)\/(x^2(sinx)^2)]=lim[(x^2-(sinx)^2)\/x^4]lim[x^2\/(sinx)^2]=lim[(x^2-(sinx)^2)\/x^4](之后的使用洛比达法则）=lim[(2x-2sinxcosx)\/(4x^3)]=lim[(2-2cos2x)\/(12x^2)]=lim[(4sin2x)\/(24x)]=(1...
当x趋向于0,求1\/sin^2-1\/x^2的极限.洛必达求导不来.
lim(1\/sin^2x-1\/x^2)=lim(x^2-sin^2x)\/(x^2sin^2x)=lim(x^2-sin^2x)\/(x^4)=lim(2x-sin2x)\/4x^3 =lim(2-2cos2x)\/12x^2 =lim4sin2x\/24x =1\/3
1\/(sinx)^2-1\/x^2的x趋于0的极限是多少,怎么算呢
lim(x→0){1\/[(sinx)^2]-1\/(x^2)} = lim(x→0){[(sinx)^2]-(x^2)}\/[(sinx)^2](x^2)= lim(x→0){[(sinx)^2]-(x^2)}\/(x^4) (0\/0)= lim(x→0)(2sinxcosx-2x)\/(4x^3)= lim(x→0)(sin2x-2x)\/(4x^3) (0\/0)= lim(x→0)(2cos2x-2)\/(1...
当x趋向于0时,求:(1\/sin^2x-1\/x^2)的极限?
通分，分母进行等价无穷小代换，注意分子不要进行代换。然后利用洛必达法则。分子要用无穷小代换的话，必须对正弦函数展开式展开到与分母同阶，舍弃更高阶的无穷小才可以，否则会发生错误。
lim(X→0)(1\/sin^2X-1\/X^2)
lim[x→0] (1\/sin²x - 1\/x²)=lim[x→0] (x²-sin²x)\/(x²sin²x)分母等价无穷小代换 =lim[x→0] (x²-sin²x)\/x⁴洛必达法则 =lim[x→0] (2x-2sinxcosx)\/(4x³)=lim[x→0] (2x-sin2x)\/(4x³)洛必...
lim(x→0) (1\/sin^2 x-1\/x^2 cos^2 x)=? "limx趋向于0。(sin方x)分之...
limx趋向于0。1\/(sin方x)-1\/（x方乘以cos方x)=lim [(sin方x)-（x方乘以cos方x)]\/[(sin方x)（x方乘以cos方x)]=lim [sin²x-x²(1-sin²x)]\/[sin²x*x²(1-sin²x)]=lim [sin²x-x²+x²sin²x)]\/[sin²...
