Seja F with rightwards arrow on top left parenthesis x comma y comma z right parenthesis equals P left parenthesis x comma y comma z right parenthe...

Question

Seja F with rightwards arrow on top left parenthesis x comma y comma z right parenthesis equals P left parenthesis x comma y comma z right parenthesis i with rightwards arrow on top plus Q left parenthesis x comma y comma z right parenthesis j with rightwards arrow on top plus R left parenthesis x comma y comma z right parenthesis k with rightwards arrow on top um campo vetorial com domínio D subset of straight real numbers cubed, de classe C to the power of 1 e S subset of D, uma superfície fechada, também de classe C to the power of 1, orientada pelo vetor normal exterior n with rightwards arrow on top. Assinale a alternativa que contenha o cálculo do fluxo do campo F with rightwards arrow on top utilizando o divergente:

a.	
double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals negative triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.

b.	
double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.

c.	
double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals negative double integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.

d.	
double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals double integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.

e.	
double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis times n with rightwards arrow on top space space d V.

Ed · Answer

Vamos analisar as opções:

a. double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals negative triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.
b. double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.
c. double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals negative double integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.
d. double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals double integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis d V.
e. double integral subscript S F with rightwards arrow on top times n with rightwards arrow on top space d A equals triple integral subscript V D i v left parenthesis F with rightwards arrow on top right parenthesis times n with rightwards arrow on top space space d V.

A resposta correta é a letra a.

Espero ter ajudado!

Seja F with rightwards arrow on top left parenthesis x comma y comma z right parenthesis equals P left parenthesis x comma y comma z right parenthe...

Cálculo Vetorial

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