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1. Let C1, C2, and C; be the oriented curves shown in the diagram to the...
Question 2. Consider a surface S in the 0 plane with three smooth boundary curves C1, C2, and C3 as shown in the diagram. Each curve is parametrised so that it is traversed in the direction shown by the arrows For a smooth vector field A(x, y, z) you are given the following results: Ca Adr =-3 C2 0.5 2.0 1.5 -0.5 (a) What is the value of the surface integral ▽ × A. ds. if we assume by convention...
4 Examples and Exercises 1. Given to the right is a vector field F(z,y), together with oriented curves C, C2, Ca, Ca, Cs, and Ce (a) Is fe F.dF positive, negative, or zero? Explain. C 4 Examples and Exercises 1. Given to the right is a vector field F(z,y), together with oriented curves C, C2, Ca, Ca, Cs, and Ce (a) Is fe F.dF positive, negative, or zero? Explain. C
Question 2 (30 points) Integrate f(x, y,2) xzv2-z2 - y2 over the path C, which consists of two curves, C1 and C2 from (1, 0, 0) to (1,0, 0), then to (-1,3, 0). Curve C1 is only half of the circle2 Curve C2 is a straight-line segment. The parametric equation for G is G: r! (t)-cos t î + sin t k, 0 π Find the line integral: Jcf(x. y,z)ds - (25 points) C2 (-1,3,0) Question 2 (30 points) Integrate...
31. For both parts of this problem, the curve C = C1 + C2 + Cg consists of the three line segments Z 2 C:(0,0,0) + (0,1,0) C2: (0,1,0) + (0,1,2) C3: (0,1,2) + (3,1,2) X and F(x, y, z) = (7y - 22,7x + 2, -2x + y) 3 Note that F is conservative! 90 (a) Compute SF. dr one of the following ways: i. Parameterization of C ii. Fundamental Theorem of Line Integrals iii. Independence of Path Clearly...
C1= 5 C2= 6 C3= 10 GCD --> Greater Common Divisor B1 a. Let x := 3C1 + 1 and let y := 5C2 + 1. Use the Euclidean algorithm to determine the GCD (x, y), and we denote this integer by g. b. Reverse the steps in this algorithm to find integers a and b with ax + by = g. c. Use this to find the inverse of x modulo y. If the inverse doesn't exist why not?...
Consider the combination of capacitors shown in the diagram, where C1 = 3.00 μF , C2 = 11.0μF , C3 = 3.00 μF , and C4 = 5.00 μF . (Figure 1)Part AFind the equivalent capacitance CA of the network of capacitors.Express your answer in microfarads.Part BTwo capacitors of capacitance C5 = 6.00 μF andC6 = 3.00 μF are added to the network, as shown in the diagram.(Figure 2) Find the equivalent capacitance CB of the new network of capacitors.Express your...
Let R be the region shown above bounded by the curve C = C1[C2. C1 is a semicircle with center at the origin O and radius 9 5 . C2 is part of an ellipse with center at (4; 0), horizontal semi-axis a = 5 and vertical semi-axis b = 3. Thanks a lot for your help:) 1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
Let C1 be the semicircle given by z = 0,y ≥ 0,x2 + y2 = 1 and C2 the semicircle given by y = 0,z ≥ 0,x2 +z2 = 1. Let C be the closed curve formed by C1 and C2. Let F = hy + 2y2,2x + 4xy + 6z2,3x + eyi. a) Draw the curve C. Choose an orientation of C and mark it clearly on the picture. b) Use Stokes’s theorem to compute the line integral ZC...
(1 point) Curves Cị and C2 are parametrized as follows: Ci is (z(t), y(t)) = (t,0) for –1<t<1 and C2 is (z(t), y(t)) = (cost, sint) for 0 <t<. Sketch, on a separate sheet of paper, the curves Cị and C2 with arrows showing their orientation. Next, suppose that F = 4x 1 +(6x + 3y) 7. Calculate Scř.dr, where is the curve given by C = C1 +C2. ScF.dñ =
Let F(x, y) = 3xyi + 2x²j and let C be the oriented curve shown below (a semicircular arc followed by three sides of a square). Evaluate the integral OF.dr, Jc both directly, and by applying Green's Theorem. [6]