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3 years ago

Determine the domain of the function. f as a function of x is equal to thirteen divided by three minus x.

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

hello :

f(x) = 13/ (x-3)

f(x) exist : x - 3 ≠ 0

x - 3 = 0 : x = 3

the domain of the function : f is D = ]-∞:3[ U] 3;+∞[

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Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

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Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

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the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
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$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

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$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

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