Suppose U(x, y) = 4x2+ 3y2 1. Calculate ∂U/∂x, ∂U/∂y 2. Evaluate these partial derivatives at...
Suppose U(x, y) = 4x2+ 3y2
1. Calculate ∂U/∂x, ∂U/∂y
2. Evaluate these partial derivatives at x= 1, y= 2
3. Calculate dy/dx for dU= 0, that is, what is the implied trade-off between x and y holding U constant?
4. Show U= 16 when x= 1, y= 2.
5. In what ratio must x and y change to hold U constant at 16 for movements away from x= 1, y= 2?
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Suppose U(x, y) = 4x2+ 3y2
1. Calculate ∂U/∂x, ∂U/∂y
2. Evaluate these partial derivatives at...
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Co...
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers are numbers.
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers...
Please help me answer these 2 questions Find all first partial derivatives. f(x, y) = 5x...
Please help me answer these 2 questions
Find all first partial derivatives. f(x, y) = 5x + 4y - 3 (, y) = f(x, y) = = Differentiate implicitly to find dy dx xx2 x + y = 5 dy II
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integra...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a)...
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
Use the transformation u = 3x + y, v=x + 3y to evaluate the given integral...
Use the transformation u = 3x + y, v=x + 3y to evaluate the given integral for the region R bounded by the lines y = - 3x + 1, y= - 3x + 3, y= - = X, and y=- -x + 2. ne lines y = – 3x+1, y = – 3x+3, y=-3x, and y=-**+2. 3 Siſ(3?+ 16 +3%) dx ay SJ (3x? + 10x9 +35) dx dy=0 (Simplify your answer.)
1. In the following function, evaluate the derivatives i-iii below: f(w,x,y,z)=3xy5 + w2z4/(16y) - xy3z/w2 ...
1. In the following function, evaluate the derivatives i-iii below: f(w,x,y,z)=3xy5 + w2z4/(16y) - xy3z/w2 i) (dF/dx)w,y,z ii) (dF/dy)w,x,z iii) [d/dz (dF/dx)w,y,z]w,x,y
Can you evaluate without Green's Theorem? If so, please show your work. Suppose that f(x, y)...
Can you evaluate without Green's Theorem?
If so, please show your work.
Suppose that f(x, y) has continuous second-order partial derivatives, and let C be the unit circle oriented counterclockwise. What is / [fx(x, y) – 2y] dx + [fy(x, y) + x] dy?
dy/ 1. Find 7dx by differentiating 2x2y = x - 3y2 implicitly. (8 pt) 2. Find...
dy/ 1. Find 7dx by differentiating 2x2y = x - 3y2 implicitly. (8 pt) 2. Find dx if y = 4x -3x (6 pt) 3. Find dx if y = cos(x2) (6 pt)
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers are numbers.
(1 point) The equations define u(x, y) and v(x, y) in terms of x and y near the point (x, y)-(1,1) and (u, v)-(1,1). Compute the partial derivatives ди du dx 0v dy dv ду Note that all answers...
Please help me answer these 2 questions
Find all first partial derivatives. f(x, y) = 5x + 4y - 3 (, y) = f(x, y) = = Differentiate implicitly to find dy dx xx2 x + y = 5 dy II
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
Use the transformation u = 3x + y, v=x + 3y to evaluate the given integral for the region R bounded by the lines y = - 3x + 1, y= - 3x + 3, y= - = X, and y=- -x + 2. ne lines y = – 3x+1, y = – 3x+3, y=-3x, and y=-**+2. 3 Siſ(3?+ 16 +3%) dx ay SJ (3x? + 10x9 +35) dx dy=0 (Simplify your answer.)
Can you evaluate without Green's Theorem?
If so, please show your work.
Suppose that f(x, y) has continuous second-order partial derivatives, and let C be the unit circle oriented counterclockwise. What is / [fx(x, y) – 2y] dx + [fy(x, y) + x] dy?
dy/ 1. Find 7dx by differentiating 2x2y = x - 3y2 implicitly. (8 pt) 2. Find dx if y = 4x -3x (6 pt) 3. Find dx if y = cos(x2) (6 pt)
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