Be the next function, Determine in points (2, -5,1):
, Determine in points (2, -5,1):
a) Divergence of the function b) Rotational of the function
Homework Answers
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Be the next function , Determine in points (2, -5,1): a) Divergence of the function b)...
Question 4(25 marks) Find the critical points of following function, then determine whether they are relative...
Question 4(25 marks) Find the critical points of following function, then determine whether they are relative maximum, relative minimum or saddle points i. f(x,y) 3x2-2xyy2- 8y [Smarks] [5marks] [5marks] iii. f(x,y)--2x + 4y-x2-4y2 + 9 b) Find the divergence and curl of the following vector fields i. F(x, y, z) = x2 yi + 2y3zj + 3zk [5marks] ii. F(x, y,z) x sin y i+4xyz j - cos 3z k [5marks]
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coo...
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
Use the divergence theorem to calculate the flux of the vector field
Use the divergence theorem to calculate the flux of the vector field \(\vec{F}(x, y, z)=x^{3} \vec{i}+y^{3} \vec{j}+z^{3} \vec{k}\) out of the closed, outward-oriented surface \(S\) bounding the solid \(x^{2}+y^{2} \leq 16,0 \leq z \leq 3\).
2. For each function, find all critical points and use the Hessian to determine whether they...
2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or saddle points. (a) f(x,y,z) = x — 2 sin x – 3yz (b) g(x, y, z) = cosh x + 4yz – 2y2 – 24 (c) u(x, y, z) = (x – z)4 – x2 + y2 + 6x2 – 22
6. Find the divergence and the curl of the vector field F(x,y,z) = 4xy'i+ xej+xyek. 6....
6. Find the divergence and the curl of the vector field \(\mathbf{F}(x, y, z)=4 x y^{2} \mathbf{i}+x e^{4 z} \mathbf{j}+x y e^{-4 z} \mathbf{k}\)
Solve with all the steps please! Calculate the divergence and the curl of the vector field...
Solve with all the steps please!
Calculate the divergence and the curl of the vector field F(x,y,z) = ( x^3y)i + (xy)j + ( 213 )k. (Where Fis a vector and i,j,k stand for the standard unit vectors)
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x,...
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = y z' i + 2yzj + 4z2k across the surface of the solid E enclosed by the paraboloid z = x2 + y2 and the plane z = 9. V
Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...
Use Gauss's Divergence Theorem to evaluate where and
S is the area limited by the cylinder and the plans
JsFinds F(x, y, z) = (x2 + cos(y2))i + (y-e)j + (22 +)k + y2 = 4 +z=2, 2=0.
Consider the three points: A = (8,7) B = (1,5) C = (5,1). Determine the angle...
Consider the three points: A = (8,7) B = (1,5) C = (5,1). Determine the angle between AB and AC. =
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
Question 4(25 marks) Find the critical points of following function, then determine whether they are relative maximum, relative minimum or saddle points i. f(x,y) 3x2-2xyy2- 8y [Smarks] [5marks] [5marks] iii. f(x,y)--2x + 4y-x2-4y2 + 9 b) Find the divergence and curl of the following vector fields i. F(x, y, z) = x2 yi + 2y3zj + 3zk [5marks] ii. F(x, y,z) x sin y i+4xyz j - cos 3z k [5marks]
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coordinate planes and x+y+z = 6
8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the...
2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or saddle points. (a) f(x,y,z) = x — 2 sin x – 3yz (b) g(x, y, z) = cosh x + 4yz – 2y2 – 24 (c) u(x, y, z) = (x – z)4 – x2 + y2 + 6x2 – 22
Solve with all the steps please!
Calculate the divergence and the curl of the vector field F(x,y,z) = ( x^3y)i + (xy)j + ( 213 )k. (Where Fis a vector and i,j,k stand for the standard unit vectors)
2. [5 POINTS] Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = y z' i + 2yzj + 4z2k across the surface of the solid E enclosed by the paraboloid z = x2 + y2 and the plane z = 9. V
Use Gauss's Divergence Theorem to evaluate where and
S is the area limited by the cylinder and the plans
JsFinds F(x, y, z) = (x2 + cos(y2))i + (y-e)j + (22 +)k + y2 = 4 +z=2, 2=0.
Consider the three points: A = (8,7) B = (1,5) C = (5,1). Determine the angle between AB and AC. =
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
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