F(x) = arctg(x)
x1 = 0.95
x0 = 1
f(x1) = f(0.95) = arctg(1 - 0.05) = arctg(x0 + dx)
dx = -0.05
f(x1)≈ f(x0) + df
df = (df/dx)*dx
df/dx = 1/(1 + x²)
|
df/dx| = 1/(1 + x0²) = 1/2
|x0
df = (df/dx)*dx = (1/2)*(-0.05) = -0.025
f(x1) ≈ f(x0) + df = arctg(1) + (-0.025) = π/4 - 0.025 ≈ 0.760
Более точное значение artcg(0.95) ≈ 0.75976275487577082892296119539998