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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.

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