Calculate the work done by the field F(x,y) = ⟨-2y, x⟩ in moving an object along the path which is the quarter circle from point (4,0) to (0,4). Use the power reducing identities to integrate. Do not use Greene's Therom, only use a single integral

Find div F and curl F if F(x,y,z)=11y6z5i-17x7z10j-6xy7k

Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the direction vector (2, -1, −2):

For the vector field G = (yey + 3 cos(3x + y))i + (xeªy + cos(3x + y)) 3, find the line integral of G along the curve C from the origin along the x-axis to the point (2,0) and then counterclockwise around the circumference of the circle x² + y² = 4 to the point (2/√2,2/√√2). So G. dr =

Find the curl of the vector field F (5x sin(y), 2y cos(x)) curl F =

Find the curl of the vector fieldF (6y cos(x), 7x sin(y)) curl F =

Sketch a slope field for = X dy dx isoclines. 3y showing a table of dy/dx and 5

Use the Product Rule to show that ( f²Y = 2ff'.

Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi).