In the nonlinear function Y=aXbZc, the parameter c measures
A. delta Y/ delta Z
B. the percent change in Y for a 1 percent change in Z
C. the elasticity of Y with respect to Z
D. both a and c
E. both b and c
In the nonlinear function Y=aXbZc, the parameter c measures A. delta Y/ delta Z B. the...
Consider the nonlinear demand function Q = X^aY^bZ^c that represents the call for three goods with prices X,Y, and Z, respectively. If a, b, and c are constants then derive the point elasticity of Q with respect to X.
(a) Given constants C, a, 8 € R, define a function by z = f(x, y) = Crºy Let dx/a, dy/y, and dz/z be the approximate relative (percent) changes in x, y, and z, respec- tively. Find the relative (percent) change in z in terms of the relative (percent) changes of a and y. (b) The total production P of a certain product depends on the amount L of labour used and the amount K of capital investment. The Cobb-Douglas...
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations dr where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them. 10 Marks (b) Consider the second order differential equation i. Show that (1) can be written as the system of ordinary differential equations (y R for...
Write a MATLAB function with the following specifications: Input parameter 1: A Input parameter 2: B Input parameter 3: C Input parameter 4: D Output parameter: Sum of the input parameters Time interval: -2T lessthanorequalto t lessthanorequalto 2T Waveform 1 to plot: y(t) = A sin(B(t - c))+D Waveform 2 to plot: y(t) = A cos(B(t - c)) + D Display two plots in vertical fashion on one figure Include all labeling on both plots. Add a grid to both...
2 (Dirac Delta Function) Using properties of the delta function and the relations discussed in class, <xx'> = 8(x – z'), ><x=1 Prove that | (x – y)8(y – 2)f(z)dydz = f(x).
Question Some values of x and y for functions A and B are sha Function A Function B X у X } 1 2 1 3 3 4 2 9 6 6 Which of the following statements is true? 9 Function A and function B are both linear Funcion A and function B are both nonlinear. Funcion Ais nonlinear and function B is linear Function A is linear and function B is nonlinear
3. Suppose we measure a quantity y as a function of a parameter z. The measurement errors ony are denoted by ơ. Given 3 measurements. 11.0 1.10 0.08 2 2.0 4.40 0.20 3 3.0 8.80 0.20 we describe the data by the model, where α is an unknown parameter. a) Define χ2 and use it to determine the best estimate, a", of a. b) Find the value of x2 at the best estimate a. Did we choose a good model...
3. Suppose we measure a quantity y as a function of a parameter z. The measurement errors ony are denoted by ơ. Given 3 measurements. 11.0 1.10 0.08 2 2.0 4.40 0.20 3 3.0 8.80 0.20 we describe the data by the model, where α is an unknown parameter. a) Define χ2 and use it to determine the best estimate, a", of a. b) Find the value of x2 at the best estimate a. Did we choose a good model...
Z- A+B+C+D Z:x component Z: y component W=A-B-C+D W :x component W: y component in the dagram tothe let Vecor A has a magnitude of 5.8 units and makes an angle of 31 degrees with respect to the positive x axis. Vector B has a magnitude of S units and makes an angle of 53.1 degrees with respect to the negative x axis. 53 319 What are the components of the resultant of: A+B
Foundations of Analysis Let X = {A, B,C,D}. ·Describe a function δ : X × X-> R that is a metric on X. . Describe a function δ : X x X-R that satisfies δ(z,x)-0 and δ(x,y)-δ(y,x) for all z, y E X but that is NOT a metric Let X = {A, B,C,D}. ·Describe a function δ : X × X-> R that is a metric on X. . Describe a function δ : X x X-R that satisfies...