用微分数计算函数值的近似值:arctan0.98

求详解!
2025-03-09 07:38:27
推荐回答(2个)
回答1:

y=arctanx
dy=y'dx=dx/(1+x^2)
在x=1, y=arctan1=π/4, dx=-0.02处,有:
dy=-0.02/(1+1)=-0.01
所以arctan0.98=π/4-0.01=0.7754.

回答2:

d(arctan x) = 1/(1+x^2) dx
arctan 0.98 = arctan (1-0.02) ≈ arctan 1 - 0.02 * d(arctan 1)
= π/4 - 0.02/2 = π/4 - 0.01 ≈ 0.775