Calculus II PASS Week 5

Divergence Operations

100

Calculate the divergence of V = 4xi - 5y²j

4 - 10y

200

Calculate the divergence of V = 10xi - 2y³j + 8k

10 - 6y²

300

Calculate the divergence of V = 15x²yi + 4xy³j + 8yz²k

30xy + 12xy² + 16yz

400

Calculate the divergence of V = 3x²y²i + (y³-2xy)j - 4xyz²k

6xy² + 3y² - 2x - 8xyz

500

Calculate the divergence of V = x²sin(y)i + 3cos(y)j + x sin(z)k

2x sin(y) - 3 sin(y) + x cos(z)

Curl Operations

100

Calculate the curl of A = x² i + 2xy j

2y k

200

Calculate the curl of A = 3x² i + 2y² j + 2x k

-2 j

300

Calculate the curl of A = x² i + 6yz³ j + 4y³z² k

12y²z² - 18yz² i

400

Calculate the curl of A = 6x² i + 6yz³ j + 4y³z² k

(x²z - 3y²)i - (2xyz - 2xy)j - 2xz k

500

Calculate the curl of A = 6sin(z) i + 4e^yx j + 8yz³ k

8z³ i - 6cos(z) j + 4e^y k

Laplacian Operations

100

Find the Laplacian of p(x,y) = x²y

2y

200

Find the Laplacian of p(x,y) = 2x³y⁴

12xy⁴ + 24x³y²

300

Find the Laplacian of p(x,y) = -x²y³ - 6x²y

-2y³ - 12y - 6x²y

400

Find the Laplacian of p(x,y) = 2x³ - 3xyz -3x²z²

12x - 6z² - 6x²

500

Find the Laplacian of p(x,y) = sin(2x)e^2y + 6e^x + z²

-4sin(2x)e^2y + 6e^x + 4sin(2x)e^2y + 2