Set up Lagrange’s equations in cylindrical coordinates for a particle of mass m in a potential field V (r, θ, z). Hint: v = ds/dt; write ds in cylindrical coordinates.

Evaluate the surface integral F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = −xi - yj + z³k, S is the part of the cone z = √x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √√x² + y² xx 0 z=4