脑袋打结了 0.
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/08 20:27:10
![](http://img.wesiedu.com/upload/5/9b/59bdc8f4068e8ec35ea11a1d7fdd3a6b.jpg)
![](http://img.wesiedu.com/upload/d/2a/d2a16c8a1fe00a1dabb6a6d46c68a73b.jpg)
![](http://img.wesiedu.com/upload/a/46/a46b106bc64ddb9660bae86756ecea04.jpg)
脑袋打结了 0.
![脑袋打结了 0.](/uploads/image/z/18893761-25-1.jpg?t=%E8%84%91%E8%A2%8B%E6%89%93%E7%BB%93%E4%BA%86+0.)
lim<x→0>(x-arcsinx)/(sinx)^3 (分母等价无穷小代换)
= lim<x→0>(x-arcsinx)/x^3 (0/0,罗必塔)
= lim<x→0>[1-1/√(1-x^2)]/(3x^2)
= lim<x→0>[√(1-x^2)-1]/[(3x^2)√(1-x^2)]
= lim<x→0>[√(1-x^2)-1]/[(3x^2)]
= lim<x→0>[(1-x^2)-1]/{[(3x^2)][√(1-x^2)+1]}
= lim<x→0>(-1)/{3[√(1-x^2)+1]} = -1/6.
2.lim<x→0>(tanx-sinx)/(xsinx^2)
= lim<x→0>tanx(1-cosx)/(xsinx^2) (等价无穷小代换)
= lim<x→0>(x*x^2/2)/x^3 = 1/2.
3.z=e^(x^2+y^2),z'<x>=2xe^(x^2+y^2),z'<y>=2ye^(x^2+y^2),
在点(1,0),z'<x>=2e,z'<y>=0,dz=2edx.
= lim<x→0>(x-arcsinx)/x^3 (0/0,罗必塔)
= lim<x→0>[1-1/√(1-x^2)]/(3x^2)
= lim<x→0>[√(1-x^2)-1]/[(3x^2)√(1-x^2)]
= lim<x→0>[√(1-x^2)-1]/[(3x^2)]
= lim<x→0>[(1-x^2)-1]/{[(3x^2)][√(1-x^2)+1]}
= lim<x→0>(-1)/{3[√(1-x^2)+1]} = -1/6.
2.lim<x→0>(tanx-sinx)/(xsinx^2)
= lim<x→0>tanx(1-cosx)/(xsinx^2) (等价无穷小代换)
= lim<x→0>(x*x^2/2)/x^3 = 1/2.
3.z=e^(x^2+y^2),z'<x>=2xe^(x^2+y^2),z'<y>=2ye^(x^2+y^2),
在点(1,0),z'<x>=2e,z'<y>=0,dz=2edx.