Question

用微分求arctan0.003近似值？

不知道怎么算

Answer 1

解：令y=arctan x，则

dy/dx=d(arctan x)=1/(1+x^2)

∵f(x+Δx)=f(x)+dy/dx·Δx

∴f(0.003)≈f(0)+1/(1+0^2)·(0.003)=arctan 0+1/(1+0^2)·(0.003)=0.003

所以，arctan0.003近似值为0.003

Answer 2

因为lim{arctanx}(当x趋近0时)=x，
所以arctan0.003=0.003

Answer 3

f(x) = arctan(x)
f(0.003) ~ f(0) + f'(0)(0.003) = 0 + 1(0.003) = 0.003

Answer 4

arctanx ≈ x
arctan0.003≈ 0.003

Answer 5

varctan0.003≈0.00299999100005