脑袋打结了 0.
1个回答

lim

(x-arcsinx)/(sinx)^3 (分母等价无穷小代换）

= lim

(x-arcsinx)/x^3 (0/0,罗必塔）

= lim

[1-1/√(1-x^2)]/(3x^2)

= lim

[√(1-x^2)-1]/[(3x^2)√(1-x^2)]

= lim

[√(1-x^2)-1]/[(3x^2)]

= lim

[(1-x^2)-1]/{[(3x^2)][√(1-x^2)+1]}

= lim

(-1)/{3[√(1-x^2)+1]} = -1/6.

2.lim

(tanx-sinx)/(xsinx^2)

= lim

tanx(1-cosx)/(xsinx^2) (等价无穷小代换）

= lim

(x*x^2/2)/x^3 = 1/2.

3.z=e^(x^2+y^2),z'

=2xe^(x^2+y^2),z'

=2ye^(x^2+y^2),

在点(1,0),z'

=2e,z'

=0,dz=2edx.

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