please use Lagrange multiplier,
and showing step by step.
Homework Answers
Add Answer to:
(1096) Let Γ be the ellipse with center at the origin that is the intersection of the plane r y +...
The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find...
The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find the points on the ellipse that are nearest to and furthest from the origin. (Justify that global extrema do exist.)
An elliptical loop of axes of length a and b, centered at origin and lying in the y − z plane car...
An elliptical loop of axes of length a and b, centered
at origin and lying in the y − z plane carries current
I. The major axis of the ellipse is the ˆy.
1. What component of A is non-zero in the x − y plane?
[A qualitative argument will sufce]
2. Find an expression for B in terms of th non-zero components of
A.
3. What is the direction of B along i) the positive x axis and ii)...
Problem 1 You are given the maximum and minimum of the function f(x, y, z) =...
Problem 1 You are given the maximum and minimum of the function f(x, y, z) = x2 - y2 on the surface x2 + 2y2 + 3z2 = 1 exist. Use Lagrange multiplier method to find them. Let us recall the extreme value theorem we discussed before the spring break: Extreme Value Theorem (For Functions Of Two Variables) If f(x,y) is continuous on a closed, bounded region D in the plane, then f attains a maximum value f(x,y) and a...
Let R be the region shown above bounded by the curve C = C1[C2. C1 is a semicircle with center at...
Let R be the region shown above bounded by the curve C = C1[C2.
C1 is a semicircle with center
at the origin O and radius 9
5 . C2 is part of an ellipse with center at (4; 0), horizontal
semi-axis
a = 5 and vertical semi-axis b = 3.
Thanks a lot for your help:)
1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
(c) Let F be the vector field on R given by F(x, y, z) = (2x...
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a ...
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) F(u, v)dudv-F(u(x, y), v(x, y))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly...
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where...
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a dif...
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...
(10 points) Let R be the region in the first quadrant bounded by the x and...
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...
The plane r+y+z= 12 intersects the paraboloid z = r2 + y2 in an ellipse. Find the points on the ellipse that are nearest to and furthest from the origin. (Justify that global extrema do exist.)
An elliptical loop of axes of length a and b, centered
at origin and lying in the y − z plane carries current
I. The major axis of the ellipse is the ˆy.
1. What component of A is non-zero in the x − y plane?
[A qualitative argument will sufce]
2. Find an expression for B in terms of th non-zero components of
A.
3. What is the direction of B along i) the positive x axis and ii)...
Problem 1 You are given the maximum and minimum of the function f(x, y, z) = x2 - y2 on the surface x2 + 2y2 + 3z2 = 1 exist. Use Lagrange multiplier method to find them. Let us recall the extreme value theorem we discussed before the spring break: Extreme Value Theorem (For Functions Of Two Variables) If f(x,y) is continuous on a closed, bounded region D in the plane, then f attains a maximum value f(x,y) and a...
Let R be the region shown above bounded by the curve C = C1[C2.
C1 is a semicircle with center
at the origin O and radius 9
5 . C2 is part of an ellipse with center at (4; 0), horizontal
semi-axis
a = 5 and vertical semi-axis b = 3.
Thanks a lot for your help:)
1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) F(u, v)dudv-F(u(x, y), v(x, y))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly...
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...
Most questions answered within 3 hours.
-
Chargaff's results yielded a molar ratio of 0.400 for A to G in
avian tubercle bacillus...
asked 38 minutes ago -
Which of the following binds ATP/ADP?
a. microfilaments
b. microtubules
c. intermediate filaments
d. microfilaments and...
asked 41 minutes ago -
Assume that the situation can be expressed as a linear cost
function. Find the cost function....
asked 2 hours ago -
(Sort ArrayList) Write the following method that sorts an
ArrayList: public static > void sort(ArrayList list)...
asked 3 hours ago -
2) A 9 volt battery is connected to a parallel plate capacitor
with an initial capacitance...
asked 2 hours ago -
Prince Equipment has to decide whether to obtain $1,000,000 of
financing by: (1) selling common stock...
asked 3 hours ago -
The terms electrical and electronic have similar but
different meanings which of the following statement is...
asked 3 hours ago -
You wish to test the claim that the mean GPA of night students
is than 2.5...
asked 4 hours ago -
A soft drink machine outputs a mean of 25 ounces per cup. The
machine's output is...
asked 5 hours ago -
Ross Co., Westerfield, Inc., and Jordan Company announced a new
agreement to market their respective products...
asked 4 hours ago -
What is the distance run by a runner 50m/hr and
60m/hr?
asked 5 hours ago -
Write a descendant selector rule that affects the <em>
element that is contained within the
<p>...
asked 5 hours ago