3. *(7 pts) Find the positively oriented simple closed curve C for which the value of the line integral is the maximum, where C is piecewise smooth. 3. *(7 pts) Find the positively oriented simp...
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)
10. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C in the xy-plane. $ 5xydx +4xdy , where C is the triangle with vertices (0,0), (5,4), and (0, 4).
Suppose is a closed curve in the plane and that -Y dr + 2? + y2 2 dy = 671 z? + y2 How many self-intersection points must have, at least? By "self-intersection point", I mean a point where the curve intersects itself other than its endpoints. For example, a simple closed curve has zero self-intersection points, and a figure 8 has one self-intersection point. Hint: If a curve has self-intersection points, then it can be divided up into a...
Let f be meromorphic functionin G and g be holomorphic function.let gamma be a simple -closed curve,positively oriented and G- contractible which does not pass through zeros or poles of f.find the integral of gf’/f over gamma intermediate of the zeros of f,and function g 4:11 AM Mon May 20 mid2-prac.pdf Done 5. (Extra credit) Let f be a meromorphic function in G and g be a holomorphic function. Let γ be a simple-closed curve, positively oriented and G-contractible which...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0, 0, 0), (2, 1, 5), (1, 1, 3), and back to the origin, in that order. Use Stokes' theorem to evaluate the integral: (Use symbolic notation and fractions where needed.) (xyz) dx + (3xy) dy + (x) dz = D .
please answer the following question so a beginner can understand. 5.3 Surface integral of vector fields 5.4 Stokes' Theorem C simple closed, positively oriented w.r.t. S 5 5.5 Divergence Theorem S is outward oriented boundary of E, Example 8. Let D be the portion of z = 1-x2-y2 inside x2 + y2-1, oriented up. F-yi+zj-xk, compute JaF -ds. 5.3 Surface integral of vector fields 5.4 Stokes' Theorem C simple closed, positively oriented w.r.t. S 5 5.5 Divergence Theorem S is...
Use Green's Theorem to evaluate the line integral along the given positively oriented curve I = Sc (2y + 7eV*)dx + (3x + cos(y2))dy, where the curve C is the boundary of the region enclosed by the parabolas y = 9x2 and x = y2
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. (3y + 7eVT) dx + (10x + 7 cos(y2)) dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2 Need Help? Read It Watch It Master It Talk to a Tutor
(d) The line integral [(x+y?)dx + (x2 + 2xy)dy, where the positively oriented curve C is the boundary of the region in the first quadrant determined by the graphs of x=0, y=x2 and y=1, can be converted to A 2xdydx 0 0 BJ 2 xdxdy 0 0 С -2x)dyda 00 D none of the above (e) Consider finding the maximum and minimum values of the function f(x, y) = x + y2 - 4x + 4y subject to the constraint...
Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5) Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5)