Question

用微分数计算函数值的近似值：arctan0.98

Answer 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.