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. The figure shows the vector field F(x, y)-< 2ry, z2 > and three curves that start and end at (1,2) and (3, 2) Explain why F dr has the same value for all three curves, and give that common va...
please answer asap (it is all the professor asked) (5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-...
please answer asap (it is all the professor asked)
(5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-1. Explain why you pick the curve you do, and how you know the integrals have the correct values. (Hint: Try picking a straight line between the origin and some simple point (a, b) that you choose later.)
(5) Consider...
Given the vector field F = <(x^2)y + (y^3) − y , 3x + 2(y^2)x +...
Given the vector field F = <(x^2)y + (y^3) − y , 3x + 2(y^2)x + e^y> For which simple closed curve in the plane does the line integral over this vector field have a maximal value? Find this value. Should we have expected the line integral over all simple closed curves to be zero?
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Com...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves...
f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves of a function f. In each case, determine whether has a local minimum, a local maximum, or neither at the labeled point. 4 3 2 Vf Vf 4 3 2 А B g(x, y) = 0 g(x, y) = 0 Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 10
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?)...
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y).
Determine whether the statement is true or false. If false, explain...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has dete...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be...
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be any simple, positively oriented, closed curve that encloses the origin. Show that: F. do 21. We will solve this problem by completing the following steps: STEP 1 Let C be a positively oriented circle of radius r with the center at the origin. Letr be so small that the circle Člies within the region enclosed by the curve C(see figure below) Compute the integral...
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...
please answer asap (it is all the professor asked)
(5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-1. Explain why you pick the curve you do, and how you know the integrals have the correct values. (Hint: Try picking a straight line between the origin and some simple point (a, b) that you choose later.)
(5) Consider...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves of a function f. In each case, determine whether has a local minimum, a local maximum, or neither at the labeled point. 4 3 2 Vf Vf 4 3 2 А B g(x, y) = 0 g(x, y) = 0 Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 10
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y).
Determine whether the statement is true or false. If false, explain...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
Consider the vector field: f (x, y)= «M(x, y), N(x, y)= v promet Let C be any simple, positively oriented, closed curve that encloses the origin. Show that: F. do 21. We will solve this problem by completing the following steps: STEP 1 Let C be a positively oriented circle of radius r with the center at the origin. Letr be so small that the circle Člies within the region enclosed by the curve C(see figure below) Compute the integral...
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...
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