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RIJEÅ ENI ZADACI IZ MATEMATIKE

RIJEÅ ENI ZADACI IZ MATEMATIKE

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18. Primjenom diferencijala približno izračunajte 1.001 10 .Rješenje:Tražimo ono što lako izračunamo, a da približno bude jednako.1 10 , bazu smo promijenili, ono što smo promijenili označimo s x.x = 1∆x = 0.001 = dxx + ∆x = 1 + 0.001 = 1.001y = x 10y ′ = 10x 9y(x + ∆x) ≈ y(x) + y ′ (x) · dxy(1 + 0.001) ≈ y(1) + y ′ (1) · dxy(1.001) ≈ 1 10 + 10 · 1 9 · 0.001y(1.001) ≈ 1.0116

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