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(d) Let (x1,x) R..9x 2 yo} (3) S is the set of combinations of (x,x2) which produce at least output level yo.Econom...
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and...
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and x2. The firm's production function describes the mathematical relationship between inputs and output, and is given by (a) Derive the degree of homogeneity of the firm's production function. 4 marks) (b) The set is the set of combinations of (xi,x2) which produce output level yo.S is a level curve of f and is referred to by economists as the...
01) Let X1, X2, ...., Xm be m independent growth observations on the first type with...
01) Let X1, X2, ...., Xm be m independent growth observations on the first type with E[X:] = u and V(x) = 02. And Let Y, Y2, ...., Yn be n independent growth observations on the second type with E[Y] = u and V(Y) = 402 And let Z1, Z2, ....,Zk be k independent growth observations on the third type with E[Z] = 2u and V(Z) = 302 Show that the estimator û = 32 - 2x - 37 is...
In space R^3, we define a scalar product by regulation 〈(x1, y1, z1), (x2, y2, z2)〉...
In space R^3, we define a scalar product by regulation 〈(x1, y1, z1), (x2, y2, z2)〉 = 2x1x2 + y1y2 + 2z1z2 + x1z2 + x2z1. (a) [10] Calculate the perpendicular projection of the point T (1, 1, 1) on the plane U in R3 with the equation x + 2y + 2z = 0 with respect to the given scalar product. (b) [10] Let φ: R^3 → R be a linear functional with φ (x, y, z) = x...
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies between the cones z = √x^2 + y^2 an...
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies
between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2.
(1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS.
(1) Let S be the part of the sphere...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F d...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
multivariable calculus please write clearly Prob. 3 (a) (10 points) Let f(x, y, z) = cos(x2)...
multivariable
calculus please write clearly
Prob. 3 (a) (10 points) Let f(x, y, z) = cos(x2) + xey2 – 2x²y?. Compute V.Of. (b) (10 points) Evaluate x² + y² + 2² <9, 220. 32 + y2 + z2 dV, where is the upper hemisphere
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y...
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y 2 -x}. Sketch the region of integration for the integral: ll -(X+Y) DA -2 -15 -105051 Compute: e-(x+y) dA and show all work.
Question 1 (32 marks) Consider a firm which produces a good, y, using two inputs or factors of production, x1 and x2. The firm's production function describes the mathematical relationship between inputs and output, and is given by (a) Derive the degree of homogeneity of the firm's production function. 4 marks) (b) The set is the set of combinations of (xi,x2) which produce output level yo.S is a level curve of f and is referred to by economists as the...
01) Let X1, X2, ...., Xm be m independent growth observations on the first type with E[X:] = u and V(x) = 02. And Let Y, Y2, ...., Yn be n independent growth observations on the second type with E[Y] = u and V(Y) = 402 And let Z1, Z2, ....,Zk be k independent growth observations on the third type with E[Z] = 2u and V(Z) = 302 Show that the estimator û = 32 - 2x - 37 is...
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies
between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2.
(1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS.
(1) Let S be the part of the sphere...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
Let F(x, y,z) = < x + y2,y + z2,z + x2 >, let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
Let F(x, y,z) = , let S be a surface with boundary C. C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). 8. a. Evaluate F dr curl F ds b.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
multivariable
calculus please write clearly
Prob. 3 (a) (10 points) Let f(x, y, z) = cos(x2) + xey2 – 2x²y?. Compute V.Of. (b) (10 points) Evaluate x² + y² + 2² <9, 220. 32 + y2 + z2 dV, where is the upper hemisphere
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y 2 -x}. Sketch the region of integration for the integral: ll -(X+Y) DA -2 -15 -105051 Compute: e-(x+y) dA and show all work.
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