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Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?)...
Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?) i + 2xy sin(xy?)j. (a) Show that F. dr is exact by finding a potential function f. (b) Is I = S, y2 sin(xy2) dx + 2xy sin(xy?) dy independent of path C? Justify your answer. (c) Use I to find the work done by the force field F that moves a body along any curve from (0,0) to (5,1).
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2,...
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(1 point) Suppose Vf2, y) = 5y sin(xy)i + 5x sin(xy)), F= f(x,y), and C is...
(1 point) Suppose Vf2, y) = 5y sin(xy)i + 5x sin(xy)), F= f(x,y), and C is the segment of the parabola y = 5x2 from the point (2,20) to (4,80). Then fF.di=
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question...
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
The vector field + (x,y) = (ycos (xy) + 2e*, xcos(xy) + 2ycos (y2)) is conservative....
The vector field + (x,y) = (ycos (xy) + 2e*, xcos(xy) + 2ycos (y2)) is conservative. Find f(x,y) such that F = Of. f=sin(x?y) + ye* + 2ys in (y? a. f = 2sin(xy) +2e* + sin(y? O b. 2 f=sin(xy) +2e* + sin(y?) OC f=sin(x+y) + 2ye* + sin(y) O d. sin (2) f=sin(x) + 2ye* + e. 2
Please answer part a and b :) Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y&#...
Please answer part a and b :)
Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y' +7) j (ii) F(x,y) = (8ye8x + cos 3ji + (e8x + 3x sin 3jj (iii) F(x,y)-7y2e7xyİ + (7 +xy) e7xyj (A) all of them (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) (ii) only (H) (i) only st Save Submit...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
so I know the answer to a) is U(x) = 4e(-2x) + 1 b) and the force is conservative, but how can I prove the force is con...
so I know the answer to a) is U(x) = 4e(-2x) + 1
b) and the force is conservative, but how can I prove the force
is conservative
Given that The potential energy at x=0 is U=5.0 The force on the particle is given by F(x) = 8 a) The potential energy function is U=-F(x) dx +C U= 8e-*dx+C U= 4(4)+c Atx = 0 U=5.0J 5=4+C C=1 The potential energy of the system as a function of the particle position...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?) i + 2xy sin(xy?)j. (a) Show that F. dr is exact by finding a potential function f. (b) Is I = S, y2 sin(xy2) dx + 2xy sin(xy?) dy independent of path C? Justify your answer. (c) Use I to find the work done by the force field F that moves a body along any curve from (0,0) to (5,1).
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
(1 point) Suppose Vf2, y) = 5y sin(xy)i + 5x sin(xy)), F= f(x,y), and C is the segment of the parabola y = 5x2 from the point (2,20) to (4,80). Then fF.di=
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
The vector field + (x,y) = (ycos (xy) + 2e*, xcos(xy) + 2ycos (y2)) is conservative. Find f(x,y) such that F = Of. f=sin(x?y) + ye* + 2ys in (y? a. f = 2sin(xy) +2e* + sin(y? O b. 2 f=sin(xy) +2e* + sin(y?) OC f=sin(x+y) + 2ye* + sin(y) O d. sin (2) f=sin(x) + 2ye* + e. 2
Please answer part a and b :)
Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y' +7) j (ii) F(x,y) = (8ye8x + cos 3ji + (e8x + 3x sin 3jj (iii) F(x,y)-7y2e7xyİ + (7 +xy) e7xyj (A) all of them (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) (ii) only (H) (i) only st Save Submit...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
so I know the answer to a) is U(x) = 4e(-2x) + 1
b) and the force is conservative, but how can I prove the force
is conservative
Given that The potential energy at x=0 is U=5.0 The force on the particle is given by F(x) = 8 a) The potential energy function is U=-F(x) dx +C U= 8e-*dx+C U= 4(4)+c Atx = 0 U=5.0J 5=4+C C=1 The potential energy of the system as a function of the particle position...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
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