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junior college 1 | H2 Maths
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Date Posted: 3 years ago
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z = xy¹·⁴
∂z/∂x = y¹·⁴ (treat the term in y as a constant)
∂z/∂y = x(1.4)y⁰·⁴ = 1.4xy⁰·⁴
(treat the term in x as a constant)
∆x = +2.3% of the original x
= 0.023x
∆y = -0.8% of the original y
= -0.008y
∂z/z (×100%) ≈ ∂z/∂x ∆x/z (×100%) + ∂z/∂y ∆y/z (×100%)
= y¹·⁴ (0.023x / xy¹·⁴) (×100%) + 1.4xy⁰·⁴ (-0.008y / xy¹·⁴) (×100%)
= 0.023 (×100%) - 0.0112 (×100%)
= 2.3% - 1.12%
= 1.18%
∂z/∂x = y¹·⁴ (treat the term in y as a constant)
∂z/∂y = x(1.4)y⁰·⁴ = 1.4xy⁰·⁴
(treat the term in x as a constant)
∆x = +2.3% of the original x
= 0.023x
∆y = -0.8% of the original y
= -0.008y
∂z/z (×100%) ≈ ∂z/∂x ∆x/z (×100%) + ∂z/∂y ∆y/z (×100%)
= y¹·⁴ (0.023x / xy¹·⁴) (×100%) + 1.4xy⁰·⁴ (-0.008y / xy¹·⁴) (×100%)
= 0.023 (×100%) - 0.0112 (×100%)
= 2.3% - 1.12%
= 1.18%
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