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Use Stokes' Theorem to Evaluate Where F(x, Y, Z) σ\sigma

Question 9

Multiple Choice

Use Stokes' Theorem to evaluate  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)    where F(x, y, z) = 11(z - y) i + 11(z2 + x) j + 11(x2 - y2) k and σ\sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.


A)  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)
B)  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)
C)  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)
D)  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)
E)  Use Stokes' Theorem to evaluate   where F(x, y, z)  = 11(z - y) i + 11(z<sup>2</sup> + x) j + 11(x<sup>2</sup> - y<sup>2</sup>) k and  \sigma  is that portion of the sphere x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 4 for which z  \ge   0. A)    B)    C)    D)    E)

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