Explore BrainMass
Share

# Vector Calculus

### Vector analysis and Stroke's theorem

Apply Stroke's theorem to evaluate the integral over C of (ydx + zdy + xdz), where C is the curve of intersection of the unit sphere x^2+y^2+z^2=1 and the plane x+y+z=0, traced anticlockwise viewed from the side of the positive x-axis

### Vector Calculus Point of Curves

F(x,y) = x^3 + y - xy + 1 a) Are there points on the curve y = (x - 1)^2 where Gradient f is perpendicular to the curve? b) Find the absolute maximum and minimum of the function in the region 1 >= x >= 0 and y >= 0.

### Vertex-Arboricity Proof

Let G be k-critical graph with respect to vertex-arboricity (k>=3). Prove that for each vertex v of G, the graph G-v is not (k-1)-critical with respect to vertex-arboricity.

### Graph and label the vertex and the line of symmetry

Graph and label the vertex and the line of symmetry. See attachment. The instructions are to graph and label the vertex and the line of symmetry. Please show all of your work. Thanks

### Vector Subspace of Vector Spaces

1. Determine whether the following sets W are vector subspaces of the vector space V. a. V=R^4, A and B are two 3 X 4 matrices. W={X is an element of R^4:Ax-3Bx=0}. b. V=C', W={f is an element of C': f(x+3)=f(x)+5 c. V=P, W={f is an element of P: f'(2)=0} d. V=C', W={f is an element of C': The integral of f(x)dx fr