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1)

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y = 1-2x²

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x=0 , dx= - 0.01

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Computing of dy :

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y = 1-2x²

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Apply derivative with respect to x

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dy/dx = 1-2*2x

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dy = (1 - 4x)dx

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Substitute x = 0 , dx = - 0.01

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dy = (1 - 4*0)(- 0.01)

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dy = - 0.01

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Computing of Δy :

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y = 1-2x²

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y(0) = 1-2*0² = 1

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y(-0.01) = 1-2(-0.01)² = 0.9998

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Δy = y(0) - y(-0.01) = 1 - 0.9998

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Δy = 0.0002

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Solution : dy = - 0.01 , Δy = 0.0002

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