1) Find the curl and the divergence of the vector field F(x.y,2)-.myityj+zk
2) Evaluate the line integral
F dr where F = xi+ yj and C is clockwise around the square with vertices
3) Find the mass of one turn of a spring with density p(r,y,2) = z. Given the shape of the spring is
4) Prove that F = (e* sin y,e* cos v) is conservative. Find its potential function. Evaluate the line integral
F dr where C is any smooth curve from (0,0) to (3,8).
5) Use Green's Theorem to evaluate the line integral. 1c(20ykar((xty/dy. C: boundary of the region lying
between the graphs of y = 0 and y =4-x².
6) Verify the Divergence Theorem by evaluating
Nas as a surface integral and as a triple integral.
Where F(x,y,2)=(x,y,z) and the solid region bounded by the coordinate planes and 2x+3y +4z = 12.
7) Find the equation of the tangent plane to the curve given by at the point(1,2,5).
8) Find the area of the sphere above the given region, F(u,v) = asinu cos vi+asinusin v}+acosuk where
0 S u S (randOsvsb.
Evaluate (r(x,y) dS. = =
10) Find the flux of F through S.
11) Verify Stokes's Theorem by showing that the following; Let C be the triangle
created by the intersection of 2x+2y+z= 6and the coordinate planes and
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