EXERCISE 1.52. If γ : [a,b]+ R2 is a closed plane curve and r den its rotation index, prove that 16 Ks(t) dt 2π otes lrohra svetem to ơranh the sim EXERCISE 1.52. If γ : [a,b]+ R2 is a close...
I don't know how to do both a
and b
16. The folium of Descartes is the curve C c R2 described by the equation a) Give a parametrization of C. Hint: Use t y/r as parameter b) Compute the area of the "leaf."
16. The folium of Descartes is the curve C c R2 described by the equation a) Give a parametrization of C. Hint: Use t y/r as parameter b) Compute the area of the "leaf."
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...