Nesta sessão, são deduzidas fórmulas específicas para alguns casos mais gerais.
• Soma ou subtração de variáveis: ω = x ± y ± z . ∂ω ∂x = 1, ∂ω ∂y = ±1, ∂ω ∂z = ±1. (A.5) e assim σ2ω = σx2+ σ2y + σz2 . (A.6) Deve ser observado que as variâncias sempre se somam, mesmo no caso de subtração de variáveis.
• Relação linear: ω = ax + b .
Admitindo que a e b são constantes isentas de erro ou com erros desprezíveis, somente a variável x é considerada para o cálculo da incerteza.
dω
dx = a . (A.7)
Substituindo na equação (A.4), obtém-se
σω2 = a2σx2 ou σω = |a|σx . (A.8) Deve ser observado que σω e σxsão quantidades positivas definidas.
No caso em que b = 0, ω = ax e a expressão (A.8) para σωpode ser simplificada dividindo-a por ω = ax:
σω ω 2 =σω x 2 ou σω ω = σxω . (A.9) • Produto ou razão de variáveis: ω = axy ou ω = ax/y .
No caso de produto de variáveis, ∂ω
∂x = ay e ∂ω
∂y = ax. (A.10)
Substituindo na expressãop (A.3) e simplificando, tem-se σω ω 2 =σx x 2 + σy y 2 . (A.11)
Este mesmo resultado vale para o caso ω = x/y.
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