Ответ:

3,002

Пошаговое объяснение:

f(x)=x⁵-2x³+2x²-x+3,   x = 1,001

f(1,001) ≈ ?

x = x₀+Δx

x₀ = 1

Δx = x-x₀ = 1,001-1 = 0,001

f `(x) = (x⁵-2x³+2x²-x+3)` = 5x⁴-6x²+4x-1+0 = 5x⁴-6x²+4x-1

f `(x₀) = f `(1) = 5-6+4-1 = 2

f(x₀) = 1-2+2-1+3 = 3

f(x+x₀) ≈ f(x₀)+f `(x₀)*Δx

f(1,001) ≈ 3+2*0,001 = 3+0,002 = 3,002