. For the function y = f(x) = x2 + x determine Eya, the elasticity of...
4. For the function y = f(x) = x2 + x determine Eyx, the elasticity of y with respect to x, at x = 4. 5. Suppose there are two types consumers in the market for commodity x, type A and B. Their demands are described, respectively, by the expressions 0 A = -4pm 140 IB = -5Pa +10 whenever Xi is nonnegative. Assuming there are 10 type A consumers and 20 type B, determine the market demand curve.
2 + (a) Determine and sketch the domain of the function f(x, y) = (x2 + y2 – 4) 9 – (x2 + y2). [7] x6 – yo (b) Evaluate lim (x,y)+(1,1) - Y [5] (c) What does it mean to say that a function f(x, y) has a relative minimum at (a,b)? [4] (d) Find all second order partial derivatives of the function f(x,y) = 22y.
x2 x2 ,Y72 f(x, y) = { ** - Y I s this function continuous at point (0,0) ? 10 y = x2
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
Graph the function f(x)-x2 +2x -4 by starting with the graph of y x2 and using transformations (shifting, stretching/compressing, and/or reflecting). Use the graphing tool to graph the function. Click to enlarge graph
7. The function z = f(x,y)= x2 +2 12 is restricted to the domain x2 + y2 =1, a circle of radius 1. Determine the global extreme points and global extreme values using the Lagrange multipliers method.
Consider the function f(x, y) = (x2 + y²)e-2. Find the correct answer for the function f Select one: A. f(x, y) takes minimum value at the point (2,0) B. f(x, y) has one minimum and one saddle point c. f(x,y) has one maximum and one saddle point D. f(x,y) has only one critical point E. f(x, y) takes negative values in the domain [0, 2] [0, 2]
6. Show that the constant-elasticity-of-substitution (CES) function is homogenous of degree U. f(x,y) = (x + y) (v/p)
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1 For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1