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5. Compute the flux (integral) of the vector field )-(7777 규) along...
10. Use the Divergence Theorem to compute the net outward flux of the vector field F=...
10. Use the Divergence Theorem to compute the net outward flux of the vector field F= <x^2, -y^2, z^2> across the boundary of the region D, where D is the region in the first octant between the planes z= 9-x-y and z= 6-x-y. The net outward flux is __. 11. Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector field F= <-7yz,2,-9xy> across the surface S, where S is the boundary of...
1. Starting with the equation a tanh y show that, for real r, y and |rl...
1. Starting with the equation a tanh y show that, for real r, y and |rl < 1, y-tanh-1 2. Compute the following derivative dtanh (sin() 3. Assume θ is a real number. Then use Euler's formula eie-cos θ + isin θ to show that coth(i0)-icot(e) 4. Use the definitions to obtain an equation for cosh(3x) in terms of cosh(x) and sinh(x) and their various products (e.g., cosh*(z), cosh(x) sinh3(x) etc.). Do not use the double-angle formula such as cosh(u+...
(a) Use surface integral(s) to calculate the flux of the vector field or through the given surface.
(a) Use surface integral(s) to calculate the flux of the vector field or through the given surface. (b) Use the divergence theorem to calculate the flux of the vector field through the given surface. 4. F(x, y, z) =x2yi - 2yzj + x2y2k; S is the surface of the rectangular solid in the first octant bounded by the planes x= 1,y=2, and z=3. Show your work and give an exact answer.
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to ev...
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t)
(a) Find the flux of the vector field F=yi-xjtk across the...
please show all work 1. DETAILS Use the Divergence Theorem to calculate the surface integral SI...
please show all work
1. DETAILS Use the Divergence Theorem to calculate the surface integral SI F.ds, that is, calculate the flux of F across S. F(x, y, z) -e'sin(y)i + e cos(y)j + yzik, S is the surface of the box bounded by the planes x=0, x= 3, y = 0, y = 4, 2 = 0, and 2 = 2 Submit Answer
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral...
Please Answer the Following Questions (SHOW ALL WORK)
1.
2.
3.
4.
Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B)...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
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....
Please answer 3 and 4 (use the answer to 3 to answer 4) and show all work. 3. Use the definition of a line integral to compute dxdy, where C is the unit circle with counterclockwise orientation. 4...
Please answer 3 and 4 (use the answer to 3 to answer
4) and show all work.
3. Use the definition of a line integral to compute dxdy, where C is the unit circle with counterclockwise orientation. 4. Explain why the computation in problem 3 shows that there is no function (x, y) with continuous first partial derivatives on 4(x,)) (0, 0) witand throu 응G )=릎(z e) onA; înother words, r r dr +亦days notexactonA. Cite specific theorem sfrom$163 A,...
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the p...
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 -
y^2)
please do all parts
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
1. Starting with the equation a tanh y show that, for real r, y and |rl < 1, y-tanh-1 2. Compute the following derivative dtanh (sin() 3. Assume θ is a real number. Then use Euler's formula eie-cos θ + isin θ to show that coth(i0)-icot(e) 4. Use the definitions to obtain an equation for cosh(3x) in terms of cosh(x) and sinh(x) and their various products (e.g., cosh*(z), cosh(x) sinh3(x) etc.). Do not use the double-angle formula such as cosh(u+...
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t)
(a) Find the flux of the vector field F=yi-xjtk across the...
please show all work
1. DETAILS Use the Divergence Theorem to calculate the surface integral SI F.ds, that is, calculate the flux of F across S. F(x, y, z) -e'sin(y)i + e cos(y)j + yzik, S is the surface of the box bounded by the planes x=0, x= 3, y = 0, y = 4, 2 = 0, and 2 = 2 Submit Answer
Please Answer the Following Questions (SHOW ALL WORK)
1.
2.
3.
4.
Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
all questions are related and need help answering!
rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
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....
Please answer 3 and 4 (use the answer to 3 to answer
4) and show all work.
3. Use the definition of a line integral to compute dxdy, where C is the unit circle with counterclockwise orientation. 4. Explain why the computation in problem 3 shows that there is no function (x, y) with continuous first partial derivatives on 4(x,)) (0, 0) witand throu 응G )=릎(z e) onA; înother words, r r dr +亦days notexactonA. Cite specific theorem sfrom$163 A,...
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 -
y^2)
please do all parts
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
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