Show all your work. There are 3 questions. The value of each question is indicated in...
10. For this problem, use the vector field Fx, y, z) = (y2, 23, ry+22) (a) 3 points Show that F is conservative. (b) 8 points Find a potential function f(x, y, :) such that F = V. (c) 4 points Evaluate SF. dr where C is any smooth curve from (1,0,-2) to (4,6,3). (d) 2 points What is the value of JF dr where is the circle 12 + y2 = 36 in the ry-plane?
Please show all the work to complete the question and explain each step, please. Thank you! Let F(x, y) e*y (y cos x - centered at (1,0) in the first quadrant, traced clockwise from (0,0) to (2, 0). And suppose that C2 is the line from (0,0) to (2,0). sin x) xexy cos xj. Suppose that C1 is the half of the unit circle (A) Use the curl test to determine whether F is a gradient vector field or not....
PLEASE ANSWER ALL PARTS AND SHOW WORK. THANK YOU! If F is a continuous vector field on an oriented surface S with unit normal vector n, then llo F.JS = : Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the zy-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, SP.d -...
calc 3 7) Fundamental Theorem of Line Integrals. a) Show that the vector field, F(x,y) = (2x - 2)i - 23e2v j, is conservative. b) Find a potential function for F. c) Evaluate F. dr if C is the path connecting the three line segments from (1,0) to (2,5) then from (2,5) to (-2,5) and finally from (-2,5) to (-1,0).
If we start with o and form F from it, we are definitely creating a co Let's start there. 4. Suppose that Q(x, y?). Let F(x,y) = Vo(x,y). a. Find Vé(x,y). F.Tds if C is the quarter unit circle from (1,0) to (0,1). b. Let F(x,y)=VQ(x,y). Find otomo 19 Il Fundamental Theorem for Line Integrals Let F be a continuous vector field on an open region R in R. There exists a potential function o with F= Vo (which means...
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
Please answer A to D. I need all of them Q6) (Bonus question) Let Г-12(-y,z)-(P(z, y), Q(z, y)). a2 y2 (a) Compute , What are the domains of these functions? (b) Sketch the curve γ1 and 72 going from (1,0) to (-1,0) along the unit circle x2 + y2-1, where γ1 goes clockwise and 72 goes counterclockwise. Sketch a (e) Compite dr al ol hat they are't sal What happened? (d) Let 3 be the path consisting of three straight...
Q4 please and thank you (3) You are given that the vector field f in Q2 is conservative. Find the corresponding potential function and use this to check the line integral evaluated in Q2. (4) Consider the vector field F(x, y) -ryi - 2j (-Fii F2j) and let C be the closed curve consisting of three segments: the straight line from (0, 0) to (1,0) followed by the circular arc from (1,0) to (0,1) followed by the straight line from...
12P SHOW ALL WORK. Support papers must be uploaded for full credit. Consider the 2-dimensional vector field F=<y.e-, -e- > and Green's Theorem (Circulation Form). Jc F. dr = S SEQ. - P, d A where F = <P. 9, R. a) Compute the 2-dimensional circulation of F. b) Evaluate one of the 2 integrals of Green's Theorem on the region bounded by the upper half of the unit circle and the line segment along the x-axis from x =...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a conservative vector field. b.) Find the potential function of F. In other words, find a scalar function f(x, y, z) such that ✓ f = 7. Please show all steps. c.) Let C be any smooth curve starting at (1,1,1) and ending at (e, e, 1). Compute (Fdi. С