if-8-error-is-made-on-x-what-is-the-percentage-error-on-x-1-5-

Question Number 190249 by alcohol last updated on 30/Mar/23

i f 8 % e r r o r i s m a d e o n x,

w h a t i s t h e p e r c e n t a g e e r r o r

o n λ x^{\frac{1}{5}} ?

Answered by mr W last updated on 30/Mar/23

y = λ x^{\frac{1}{5}}

\frac{Δ y}{Δ x} \approx \frac{d y}{d x} = \frac{λ}{5} x^{- \frac{4}{5}}

\frac{Δ y}{y} = \frac{\frac{λ}{5} x^{- \frac{4}{5}}}{λ x^{\frac{1}{5}}} = \frac{Δ x}{5 x} = \frac{8 %}{5} = 1 . 6 %

i . e . e r r o r o n λ x^{\frac{1}{5}} i s 1 . 6 % .

Commented by mr W last updated on 30/Mar/23

o r

y = λ x^{\frac{1}{5}}

y + Δ y = λ {(x + Δ x)}^{\frac{1}{5}} \approx λ x^{\frac{1}{5}} (1 + \frac{Δ x}{5 x}) = y (1 + \frac{Δ x}{5 x})

Δ y \approx y \frac{Δ x}{5 x}

\frac{Δ y}{y} \approx \frac{Δ x}{5 x} = \frac{8 %}{5} = 1 . 6 %

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