Question

17-22 Find div F and curl F. 17. F(x, y, z) = x^2i - 2j + yzk 18. F(x, y, z) = xz^3i + 2y^4x^2j + 5z^2yk 19. F(x, y, z) = 7y^3z^2i - 8x^2z^5j - 3xy^4k 20. F(x, y, z) = e^{xy}i - cos yj + sin^2 zk 21. F(x, y, z) = 1 / sqrt(x^2 + y^2 + z^2) * (xi + yj + zk)

          17-22 Find div F and curl F.
17. F(x, y, z) = x^2i - 2j + yzk
18. F(x, y, z) = xz^3i + 2y^4x^2j + 5z^2yk
19. F(x, y, z) = 7y^3z^2i - 8x^2z^5j - 3xy^4k
20. F(x, y, z) = e^{xy}i - cos yj + sin^2 zk
21. F(x, y, z) = 1 / sqrt(x^2 + y^2 + z^2) * (xi + yj + zk)

17-22 Find div F and curl F.
17. F(x, y, z) = x^2i - 2j + yzk
18. F(x, y, z) = xz^3i + 2y^4x^2j + 5z^2yk
19. F(x, y, z) = 7y^3z^2i - 8x^2z^5j - 3xy^4k
20. F(x, y, z) = e^xyi - cos yj + sin^2 zk
21. F(x, y, z) = 1 / sqrt(x^2 + y^2 + z^2) * (xi + yj + zk)

Added by Brittany J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Harsha M

03/26/2022

Step 1

Divergence of \( F \) is given by: \[ \nabla \cdot F = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(-2) + \frac{\partial}{\partial z}(yz) \] Show more…

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Thanks for your feedback!

17. F = x^2i - 2j + yzk 18. F = xz^3i + 2y^4x^2j + 5z^2yk 19. F = 7y^3z^2i - 8x^2z^5j - 3xy^4k 20. F = e^{xy}i - cos yj + sin^2 zk 21. F = 1 / sqrt(x^2 + y^2 + z^2) * (xi + yj + zk)