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4. The figure below shows a cylinder with walls y = x2 and x = y2 truncated by the plane 0 0 (i) ...
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b)...
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2), c) the parabola z t,y 1
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the par...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1 1 point) Find the...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 inter...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem.
9. The upper half of the ellipsoid tr + ty?...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1, above the xy-plane, and below the...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
s is the surface X2 16 (y2+22) TE 0,4] obtained by rotating the function c : 4 y about the x-axis for x є 04 Given the...
s is the surface X2 16 (y2+22) TE 0,4] obtained by rotating the function c : 4 y about the x-axis for x є 04 Given the vector field: E-(12yz-22)(22z+3y)j+(3z-22y)k, Calculate the outward flux of E through surface S. That is find 3 z JEdS Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 JSkipped
s is the surface X2 16...
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem b...
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds.
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds.
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, ...
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
5)Evaluate f (x2-y)dr + (y2 +x)dy along a) a straight line from (0.1) to (1,2), b) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2), c) the parabola z t,y 1
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
9. The upper half of the ellipsoid tr + ty? + Z2-1 intersects the cylinder x2 + y2-y 0 in a curves C. Calculate tfe circulation of v y'i+y+3i k around C by using Stokes Theorem. x2 + y2 intersec ts the plane z y in a curve C. Calculate the circulation 10. The paraboloid z of v 2zi+ x j + y k around C by using Stokes Theorem.
9. The upper half of the ellipsoid tr + ty?...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
s is the surface X2 16 (y2+22) TE 0,4] obtained by rotating the function c : 4 y about the x-axis for x є 04 Given the vector field: E-(12yz-22)(22z+3y)j+(3z-22y)k, Calculate the outward flux of E through surface S. That is find 3 z JEdS Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 JSkipped
s is the surface X2 16...
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds.
circle x2 + y2-9 in the x-y plane, oriented counter-clockwise. Let F(x, y, z)-(y,-x,0) Verify Stokes' Theorem by calculating a) surl(F) nds and b) F Tds.
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
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