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leralitvia
@leralitvia
August 2022
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Найти приращение функции при приращении аргумента на Δx.
y = x2 – 8x
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Verified answer
Y(x)=x²-8x
Δx=x-x₀
x₀=x-Δx
y(x₀)=(x-Δx)²-8(x-Δx)=x²-2xΔx+(Δx)²-8x+8Δx
Δy=y(x)-y(x₀)
Δy=(x²-8x)-(x²-2xΔx+(Δx)²-8x+8Δx)=x²-8x-x²+2xΔx-(Δx)²+8x-8Δx=
=2xΔx-(Δx)²-8Δx
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Answers & Comments
Verified answer
Y(x)=x²-8xΔx=x-x₀
x₀=x-Δx
y(x₀)=(x-Δx)²-8(x-Δx)=x²-2xΔx+(Δx)²-8x+8Δx
Δy=y(x)-y(x₀)
Δy=(x²-8x)-(x²-2xΔx+(Δx)²-8x+8Δx)=x²-8x-x²+2xΔx-(Δx)²+8x-8Δx=
=2xΔx-(Δx)²-8Δx