Consider the following function
Consider the following function:
$$ \frac{y^{\lambda}-1}{\lambda}=\alpha+\beta \frac{x^{\lambda}-1}{\lambda}+u $$
Using l'Hôpital's rule show that for \(\lambda=1\) the function is linear and for \(\lambda=0\) logarithmic.
Homework Answers
Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1....
Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1. That is, x + y = 1. Given this constraint, which of the following functions of x is equivalent to the original function f(x,y)=xy? $$ \begin{aligned} &\tilde{f}(x)=1-x \\ &\tilde{f}(x)=x-x^{2} \\ &\tilde{f}(x)=x+x^{2} \\ &\widetilde{f}(x)=x^{2} \end{aligned} $$The langrange method can also be used to solve this constrained maximization problem.The langrangian for this constrained maximization problem is _______ Which of the following are the first order conditions for a critical...
The one-dimensional Schrindinger wave equation for a particle in a potential field
The one-dimensional Schrindinger wave equation for a particle in a potential field \(V=\) \(\frac{1}{2} k x^{2}\) is$$ -\frac{h^{2}}{2 m} \frac{d^{2} \psi}{d x^{2}}+\frac{1}{2} k x^{2} \psi=E \psi(x) $$(a) Lsing \(\xi=\alpha x\) and a constant \(\lambda\), we have$$ a=\left(\frac{m k}{A^{2}}\right)^{1 / 4}, \quad A=\frac{2 L}{A}\left(\frac{m}{k}\right)^{1 / 2} $$show that$$ \frac{d^{2} y(\xi)}{d \xi^{2}}+\left(\lambda-\xi^{2}\right) \psi(\xi)=0 $$(b) Substituting$$ \psi(\xi)=y(\xi) e^{2} / 2 $$show that \(y(t)\) satisfies the Hermite di fferential equation.
3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced in the previous q...
3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced in the previous question. Show that | -1 u(E)dE-: 0. (Hint: you can do this without evaluating the function.) Determine the values of the midpoint rule,the simple trapezoidal rule (with two points) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? [10pts]
3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced...
Consider the function
Consider the function \(f(x, y)=\frac{x y}{x^{2}+y^{2}}\) if \((x, y) \neq(0,0)\)$$ =0 \text { if }(x, y)=(0,0) $$Which one of the statement is incorrect.Select one:a. \(f(x, y)\) is differentiable everywhere.b. \(f(x, y)\) is differentiable everywhere except at the origin.c. \(f(x, y)\) is not continuousd. First partial derivatives \(f(x, y)\) exist.e. \(\lim _{(x, y) \rightarrow(0,0)} \frac{x y}{x^{2}+y^{2}}\) does not exist.
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the...
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
Complete parts a-e. 1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint:...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
LISP lambda calculate， expression 3) Consider reducing the following λ-expression to its normal form. Show the...
LISP lambda calculate， expression
3) Consider reducing the following λ-expression to its normal form. Show the sequence of normal order reductions the sequence of applicative order reductions. · · 4) Consider the following function: Fx) ifx-0) then return 0 else return x+1 a) Express F as a lambda calculus expression b) Evaluate F(0) as a lambda expressiorn c) Evaluate F(1) as a lambda expression HINT: Use the representations introduces in Section 10. 5) Describe a function to compute the sum...
please help me with ‘b’ (a) y 0 O linear function, of the form fx) mx+b O trigonometric function, of the form fx) - a cos(bx) + c O exponential function, of the form rx)-a ebx+ C O logarithmic fun...
please help me with ‘b’
(a) y 0 O linear function, of the form fx) mx+b O trigonometric function, of the form fx) - a cos(bx) + c O exponential function, of the form rx)-a ebx+ C O logarithmic function, of the form fx) a In(bx)+ c O root function, of the form x) a Vbx c (b) y 0. O logarithmic function, of the form x) a In(bx) +c trigonometric function, of the form rx) a cos(bx) + c...
1-Given the function:
1-Given the function: \(y=\frac{x^{2}-3 x-4}{x^{2}-5 x+4}\), decide if \(f(x)=y\) is continuous or has a removable discontinuity, and find horizontal tond vertical asymptotes.2 A-Use the definition \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) to prove that derivative of \(f(x)=\sqrt{4-x}\) is \(\frac{-1}{2 \sqrt{4-x}}\)2 B- Evaluate the limit \(\lim _{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\) for the given value of \(x\) and function \(f(x) .\)$$ f(x)=\sin x, \quad x=\frac{\pi}{4} $$3-Given the function: \(y=(x+4)^{3}(x-2)^{2}\), find y' and classify critical numbers very carefully using first derivative tess...
MATLAB Problem HW7P2 (20 points) (5 pts) Write a user-defined MATLAB function called HW7P2_fn for the...
MATLAB Problem
HW7P2 (20 points) (5 pts) Write a user-defined MATLAB function called HW7P2_fn for the following math function 3 o-0.47x The input to the function is x and the output is y. Write the function such that x can be an array (use element-by-element operations) (15 pts) Use the function in (a) the command window to calculate y(-2) and y(5) (b) a script file HW7P2.m to determine y(x) for 0.001 Sx S 10 with 1000 points. Hint: Use the...
3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced in the previous question. Show that | -1 u(E)dE-: 0. (Hint: you can do this without evaluating the function.) Determine the values of the midpoint rule,the simple trapezoidal rule (with two points) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? [10pts]
3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced...
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
LISP lambda calculate， expression
3) Consider reducing the following λ-expression to its normal form. Show the sequence of normal order reductions the sequence of applicative order reductions. · · 4) Consider the following function: Fx) ifx-0) then return 0 else return x+1 a) Express F as a lambda calculus expression b) Evaluate F(0) as a lambda expressiorn c) Evaluate F(1) as a lambda expression HINT: Use the representations introduces in Section 10. 5) Describe a function to compute the sum...
please help me with ‘b’
(a) y 0 O linear function, of the form fx) mx+b O trigonometric function, of the form fx) - a cos(bx) + c O exponential function, of the form rx)-a ebx+ C O logarithmic function, of the form fx) a In(bx)+ c O root function, of the form x) a Vbx c (b) y 0. O logarithmic function, of the form x) a In(bx) +c trigonometric function, of the form rx) a cos(bx) + c...
MATLAB Problem
HW7P2 (20 points) (5 pts) Write a user-defined MATLAB function called HW7P2_fn for the following math function 3 o-0.47x The input to the function is x and the output is y. Write the function such that x can be an array (use element-by-element operations) (15 pts) Use the function in (a) the command window to calculate y(-2) and y(5) (b) a script file HW7P2.m to determine y(x) for 0.001 Sx S 10 with 1000 points. Hint: Use the...
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