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What is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$, for the function $\phi = 3x^2 + 4y^2 + 5z^2$?
What is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$, for the function $\phi = 3x^2 + 4y^2 + 5z^2$?
- 24π
- 72π (correct)
- 12π
- 48π
For the function $\phi = x^3 + y^3 + z^3$, what is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$?
For the function $\phi = x^3 + y^3 + z^3$, what is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$?
- 8π
- 12π
- 20π
- 16π (correct)
If the function $\phi = 2x^2 + 3y^2 + 6z^2$, what is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$?
If the function $\phi = 2x^2 + 3y^2 + 6z^2$, what is the value of the surface integral $\oiint\limits_{S} \mathbf{n} \cdot \nabla\phi dS$, where $S$ is the surface of a sphere of unit radius and $\mathbf{n}$ is the outward unit normal vector on $S$?
- 36π
- 24π (correct)
- 48π
- 12π
What is the Fourier series expansion of 𝑥 ଷ in the interval −1 ≤ 𝑥 < 1 with periodic continuation?
What is the Fourier series expansion of 𝑥 ଷ in the interval −1 ≤ 𝑥 < 1 with periodic continuation?
What is the period of the Fourier series expansion of 𝑥 ଷ in the interval −1 ≤ 𝑥 < 1?
What is the period of the Fourier series expansion of 𝑥 ଷ in the interval −1 ≤ 𝑥 < 1?
What is the range of the Fourier coefficients in the series expansion of 𝑥 ଷ?
What is the range of the Fourier coefficients in the series expansion of 𝑥 ଷ?
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