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tion 2. In class we proved that if proved that if ſc F. dr is independent...
Question 2. In class we proved that if proved that if /F. dr is independent of...
Question 2. In class we proved that if proved that if /F. dr is independent of path in a domain D, then F. dr = 0 for any closed curve C CD. F Prove the converse: ie, prove that if ſc F. dr = 0 for any closed curve C C D, then ScF. dr is independent of path in D. Hint: Choose two points A and B in D, and form two paths Cį and C2 from A to...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curv...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
please give some explanation to each step 15 Total Question 3 Let F: R3R3 be any...
please give some explanation to each step
15 Total Question 3 Let F: R3R3 be any C2 vector field. 3(a). Prove that the divergence of the curl of F is zero. /4 marks 3(b). For F as defined above, a misguided professor claims that for any closed curve C, F dr 0 because of the argument: (x F)ds F-dr div (eurl F) dV X 0-APO by using Stokes' theorem, the divergence theorem, and then part (a) for an appropriately chosen...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (8x-8y+62)(i + j) and C is the triangle with vertices (0,0,0), (8, 0, 0), (8,2,0), traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r (t) that traverses the path from start to end for 0sts 1 On Ci from (0,0, 0) to (8,0,0), r(t) = <8t,0,0> On C2 from (8, 0, 0)...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and li...
I need to solve q3. Please write clean and readable. Thanks.
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and line integrals to prove the following theorem. Theorem 1. Let S denote the closed unit ball in R2, that is, S := {x E R2 : 1-1 Assume that F : S → R2 is a function of class C2 such that F(x) = x for all x E as. Then it cannot...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j + (cy + eylz cos.) k. (a) Show that F is a gradient vector field by finding a function o such that F = Vº. (b) Show that F is conservative by showing for any loop C, which is a(t) for te (a, b) satisfying a(a) = a(6), ff.dr = $. 14. dr = 0. Hint: the explicit o from (a) is not needed....
1) Discuss the company's top risks? 2) Discuss whether the company treats risk reactively or proactively?...
1) Discuss the company's top risks? 2) Discuss whether the company treats risk reactively or proactively? 3) Do you observe a lack of understanding of potential exposures? 4) Does the company focus on internal risks or external risks? 5) Do you think the company is well prepared to respond to potential risks? Orange County he t die Following the debocie Orange County o dmorych of control procedures and financial gove nonce and d e setof o n policies December 1994...
Question 2. In class we proved that if proved that if /F. dr is independent of path in a domain D, then F. dr = 0 for any closed curve C CD. F Prove the converse: ie, prove that if ſc F. dr = 0 for any closed curve C C D, then ScF. dr is independent of path in D. Hint: Choose two points A and B in D, and form two paths Cį and C2 from A to...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
please give some explanation to each step
15 Total Question 3 Let F: R3R3 be any C2 vector field. 3(a). Prove that the divergence of the curl of F is zero. /4 marks 3(b). For F as defined above, a misguided professor claims that for any closed curve C, F dr 0 because of the argument: (x F)ds F-dr div (eurl F) dV X 0-APO by using Stokes' theorem, the divergence theorem, and then part (a) for an appropriately chosen...
(2 pts) Calculate the circulation, rF dr, in two ways, directly and using Stokes' Theorem. The vector field F (8x-8y+62)(i + j) and C is the triangle with vertices (0,0,0), (8, 0, 0), (8,2,0), traversed in that order. Calculating directly, we break C into three paths. For each, give a parameterization r (t) that traverses the path from start to end for 0sts 1 On Ci from (0,0, 0) to (8,0,0), r(t) = <8t,0,0> On C2 from (8, 0, 0)...
True or False Determine whet her the statement is true or false, and circle the correct answer. Each question is worth 2 points. (1) If F is a vector field and C is an oriented curve, then F dr must be less than zero. F (2) It is possible that for a certain vector field F and piecewise smooth oriented path C we have/. F. dr-2i-Sj. (3) Suppose d·is the unit square joining the points (0,0), (1,0), (1,1), (0.1) oriented...
I need to solve q3. Please write clean and readable. Thanks.
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and line integrals to prove the following theorem. Theorem 1. Let S denote the closed unit ball in R2, that is, S := {x E R2 : 1-1 Assume that F : S → R2 is a function of class C2 such that F(x) = x for all x E as. Then it cannot...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j + (cy + eylz cos.) k. (a) Show that F is a gradient vector field by finding a function o such that F = Vº. (b) Show that F is conservative by showing for any loop C, which is a(t) for te (a, b) satisfying a(a) = a(6), ff.dr = $. 14. dr = 0. Hint: the explicit o from (a) is not needed....
1) Discuss the company's top risks? 2) Discuss whether the company treats risk reactively or proactively? 3) Do you observe a lack of understanding of potential exposures? 4) Does the company focus on internal risks or external risks? 5) Do you think the company is well prepared to respond to potential risks? Orange County he t die Following the debocie Orange County o dmorych of control procedures and financial gove nonce and d e setof o n policies December 1994...
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