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9 Exercise 1. For the following functions, which you previously analyzed for Homework 16, calculate the...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your step...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your steps clearly Define the definiteness of the following A-[1 5 a. b. 1 4 6 d. D= -2 3 1 -2 1 2 E 2 -3 1 2. Is the function f(x,y) - 7x2 + 4xy + y2 positive definite, negative definite, positive semidefinite or negative semidefinite? Find the extreme values for the following functions and identify whether they are local maximum, local minimum, and saddle...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z =...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
1. (based on exercise 6.5 on page 301) For each of the following functions, find their first and ...
1. (based on exercise 6.5 on page 301) For each of the following functions, find their first and second derivatives, and use these to find the function's critical points. Characterize each critical point as a local minimum, maximum, saddle point, or something else. (a) f(x, y-x2-4ry + y2 (b) f(x,y)=x4-4xy+94. (c) f(x, y) 2x3-3z2-62y(x-y-1). (d) f(x, y) = y4-v2 + 2y(1-x) + 1. (e) For the function in item 1d, what is the steepest descent direction at (x, y) (0,0)?...
Start this exercise on a new sheet of paper. For every question, you need to present...
Start this exercise on a new sheet of paper. For every question, you need to present a clear and logical solution, show your computations, and present a clean and legible work. Write your final answer in a box or highlight it. Consider the function 3 f(x, y) 222 +2° + 3y?. 1. Find the local minima, local maxima, and saddle points of f, and the points where they occur. 2. Use the method of Lagrange multipliers to find the global...
Calculus III 1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z...
Calculus III
1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal a...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the...
Problem 1. (20) The purpose of this exercise is for you to get familiar with MATLAB...
Problem 1. (20) The purpose of this exercise is for you to get familiar with MATLAB and some of its capabilities. We have seen in class that, for a positive integer n and data {(rj, yj)|j= 0,...n}, the matrix system produces the coefficients of the polynomial Pn(x) coc1x++ cn&" that interpolates the data, where [Vn]ij = x;_{ for 1 < i,j <n+1. Let r j/n, giving a uniformly spaced set of n 1 points in [0, 1]. Write a MATLAB...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1...
2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1 u(x,y) = 2x+2y C2 u(x,y) = x^3/4y^1/4 C3 u(x,y) = min(x,y) C4 u(x,y) = min(4x,3y) On the appropriate graph, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6) and (8,8), AND label the utility level of each curve. Hint: Each grid should have 4 curves on it representing the same preferences but with different utility levels. 3. In the following parts,...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your steps clearly Define the definiteness of the following A-[1 5 a. b. 1 4 6 d. D= -2 3 1 -2 1 2 E 2 -3 1 2. Is the function f(x,y) - 7x2 + 4xy + y2 positive definite, negative definite, positive semidefinite or negative semidefinite? Find the extreme values for the following functions and identify whether they are local maximum, local minimum, and saddle...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
1. (based on exercise 6.5 on page 301) For each of the following functions, find their first and second derivatives, and use these to find the function's critical points. Characterize each critical point as a local minimum, maximum, saddle point, or something else. (a) f(x, y-x2-4ry + y2 (b) f(x,y)=x4-4xy+94. (c) f(x, y) 2x3-3z2-62y(x-y-1). (d) f(x, y) = y4-v2 + 2y(1-x) + 1. (e) For the function in item 1d, what is the steepest descent direction at (x, y) (0,0)?...
Start this exercise on a new sheet of paper. For every question, you need to present a clear and logical solution, show your computations, and present a clean and legible work. Write your final answer in a box or highlight it. Consider the function 3 f(x, y) 222 +2° + 3y?. 1. Find the local minima, local maxima, and saddle points of f, and the points where they occur. 2. Use the method of Lagrange multipliers to find the global...
Calculus III
1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010 Revised by Prof. Africk and Prof. Kostadinov Fall 2015, Spring 2016, #1 Identify the horizontal and vertical asymptotes of the following functions using the limit definitions: 2x2 o) yA- #2 Find the derivatives of the following functions using the definition of derivative: a) f(x)-2x-5x #3 Find the derivative v dr of the following functions, using the derivative rules: b) f(x)--2x +3x-4 #4 Find the...
Problem 1. (20) The purpose of this exercise is for you to get familiar with MATLAB and some of its capabilities. We have seen in class that, for a positive integer n and data {(rj, yj)|j= 0,...n}, the matrix system produces the coefficients of the polynomial Pn(x) coc1x++ cn&" that interpolates the data, where [Vn]ij = x;_{ for 1 < i,j <n+1. Let r j/n, giving a uniformly spaced set of n 1 points in [0, 1]. Write a MATLAB...
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