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orter Homeworks: Classify the following seconda linear PÞE: ( ) x + 2+ u f(4-1) =...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the...
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE:...
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE: (b) Use your classification from (a) to use an appropriate method in the following problem. Be sure to clearly label steps to maximize your score Find an explicit solution of +y=sin(x). Explicit Solution: (c) Give the largest interval over which the general solution is defined. (d) Are there any transient terms in the general solution? If yes, what are they?
1. For the following two systems of linear equations answer the questions 4 + x +...
1. For the following two systems of linear equations answer the questions 4 + x + 2xy + 2x - 6 3x + 2x + 3x3 + 3x = 11 2x + 2x + 3.5+ 2x- 9 2x + 2x+4x3+5x - 13 3x, +2, +4x3+4x-13 3x+3x+3x2+2x, -11 (1) Solve the above systems of linear equations using naive Gauss elimination (b) solve the above systems of linear equations using Gauss elimination with partial pivoting . Axb 2. For the following matrix...
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4...
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g 12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor u(x) = expl (1) Given the equation xy' + (1 +4x) y = 10xe 4* find y(x) = (2) Then find an explicit general solution with arbitrary constant C. y = (3) Then solve the initial value problem with y(1) = e-4 y =
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear...
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear or nonlinear. Briefly explain your answer (a) x+y" + xy' + (x2 – v2)y=0 where v is a parameter (b) më+ ki = ač – bì3 where m, k, a, b are constants (c) T = -k(T – A) where k, A are constants. (2) [3+3+4 marks] Consider the equation ay = y(y2 – 4u) where u is a parameter. (a) For u =...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to the function f at a = (ii) Graph f and L on the same set of axes. (iii) Based on the graphs of part (ii), state whether linear approximations to f near a are underestimates or overestimates. (iv) Compute f"(a) to confirm your conclusion.
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1...
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
8.2 (2). Consider the linear equation Y'(x) = XY (2) + (1 - 1) cos(x) -...
8.2 (2). Consider the linear equation Y'(x) = XY (2) + (1 - 1) cos(x) - (1+) sin(x), quady (0) = 1 The true solution is Y (1) = sin(1) + cos(r). Solve this problem using Euler's method with several values of and h, for 0 <<<10. Comment on the results. (a) X = -1; h=0.5, 0.25, 0.125 (b) X = 1; h = 0.5, 0.25, 0.125 (c) = -5; h=0.5, 0.25, 0.125, 0.0625 (d) = 5; h= 0.0625
4. Assume a utility function described by u(x,y)=2/xy. a. Given the utility function, u(x,y)=2xy, sketch the indifference curves for u = 50, 72 and 98. e indifference Carved forbise banta un b. Sketch budget constraint of 5x +10y = 30. Label intercepts (where it crosses the axes). 00:0 VE c. Solve for calculate) the optimal bundle (x, y) and sketch the optimal solution.
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE: (b) Use your classification from (a) to use an appropriate method in the following problem. Be sure to clearly label steps to maximize your score Find an explicit solution of +y=sin(x). Explicit Solution: (c) Give the largest interval over which the general solution is defined. (d) Are there any transient terms in the general solution? If yes, what are they?
1. For the following two systems of linear equations answer the questions 4 + x + 2xy + 2x - 6 3x + 2x + 3x3 + 3x = 11 2x + 2x + 3.5+ 2x- 9 2x + 2x+4x3+5x - 13 3x, +2, +4x3+4x-13 3x+3x+3x2+2x, -11 (1) Solve the above systems of linear equations using naive Gauss elimination (b) solve the above systems of linear equations using Gauss elimination with partial pivoting . Axb 2. For the following matrix...
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g 12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor u(x) = expl (1) Given the equation xy' + (1 +4x) y = 10xe 4* find y(x) = (2) Then find an explicit general solution with arbitrary constant C. y = (3) Then solve the initial value problem with y(1) = e-4 y =
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear or nonlinear. Briefly explain your answer (a) x+y" + xy' + (x2 – v2)y=0 where v is a parameter (b) më+ ki = ač – bì3 where m, k, a, b are constants (c) T = -k(T – A) where k, A are constants. (2) [3+3+4 marks] Consider the equation ay = y(y2 – 4u) where u is a parameter. (a) For u =...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to the function f at a = (ii) Graph f and L on the same set of axes. (iii) Based on the graphs of part (ii), state whether linear approximations to f near a are underestimates or overestimates. (iv) Compute f"(a) to confirm your conclusion.
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
8.2 (2). Consider the linear equation Y'(x) = XY (2) + (1 - 1) cos(x) - (1+) sin(x), quady (0) = 1 The true solution is Y (1) = sin(1) + cos(r). Solve this problem using Euler's method with several values of and h, for 0 <<<10. Comment on the results. (a) X = -1; h=0.5, 0.25, 0.125 (b) X = 1; h = 0.5, 0.25, 0.125 (c) = -5; h=0.5, 0.25, 0.125, 0.0625 (d) = 5; h= 0.0625
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