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3. Consider the function()x(x-1/2)(1) for z E 0,1]. Determine the transformed function u() introduced in the previous q...
. Consider the function v(r) r(r 1/2) (r-1) for r e (0, 1]. Determine the transformed...
. Consider the function v(r) r(r 1/2) (r-1) for r e (0, 1]. Determine the transformed function u(E) introduced in the previous question. Show that 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 point s) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? 10pts
. Consider the function v(r) r(r 1/2) (r-1) for...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10 7 (a) Plot the function f(x) within the interval [20, 100] using 101 samples (b) Calculate the area under the curve of f(x) within the interval [20, 100] using the analytical solution of the integral. (c) Calculate the area under the curve of f(x) within the interval [20, 100] using trapezoidal numerical integration (hint: "trapz") (d) Calculate the area under the curve...
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables....
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is 0.5 x=1 0.5 x=-1 Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y are independent. Meanwhile, let Z = XY. N(0,1). X and Y (a) What is the Expectation (mean value) of X? 3pts (b) Are Y and Z independent? (Just clarify, do not need to prove) [2pts c)...
5. Determine the characteristic function Ø(u) = E(exp(ju? x)] of the Gaussian random vector X having...
5. Determine the characteristic function Ø(u) = E(exp(ju? x)] of the Gaussian random vector X having mean m= [1 3]T and covariance matrix C = [? 2]
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. ...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
1. Consider the transformed function g(x)=-3 +2 of the function (x Then answer the following: a....
1. Consider the transformed function g(x)=-3 +2 of the function (x Then answer the following: a. List the sequence of transformations in a correct order. b. Write the equation of the horizontal asymptote. c. Find the vertical intercept of g(x) written as an ordered pair. d. Find the horizontal intercept algebraically and leave it in an exact form (not decimal approximation). e. Sketch the graph of g(x) 2. Solve the following equations algebraically for x : a. 16-) = 82-1...
Consumer's surplus: A consumer has the utility function U(x,y) =e^((ln(X)+Y)^1/3) where X is the good in...
Consumer's surplus: A consumer has the utility function U(x,y) =e^((ln(X)+Y)^1/3) where X is the good in concern and Y is the money that can be spent on all other goods. (So the price of Y is normalized to be 1). The income of this consumer is 100. (a) (10pts) Derive the demand function of x for this consumer. Make sure that at every price of x, the consumer always has enough income to buy the amount of x as indicated...
Previous Problem Results for this submission Entered (e^x)"I((e^x)+2)*(x+1)^(-2)]*[x*(e^e)+2] -e/((ez The answer above is NOT correct. (1...
Previous Problem Results for this submission Entered (e^x)"I((e^x)+2)*(x+1)^(-2)]*[x*(e^e)+2] -e/((ez The answer above is NOT correct. (1 point) Calculate the derivative using the appropriate rule or combination of rules. (ex + 2)(2+1) f'(x)= (-eº X (e^x+2)(X+1)) -2)*(xe°e+2). Preview My Answers Submit Answers Your score was recorded You have attempted this problem 10 times att earch
. Consider the function v(r) r(r 1/2) (r-1) for r e (0, 1]. Determine the transformed function u(E) introduced in the previous question. Show that 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 point s) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? 10pts
. Consider the function v(r) r(r 1/2) (r-1) for...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10 7 (a) Plot the function f(x) within the interval [20, 100] using 101 samples (b) Calculate the area under the curve of f(x) within the interval [20, 100] using the analytical solution of the integral. (c) Calculate the area under the curve of f(x) within the interval [20, 100] using trapezoidal numerical integration (hint: "trapz") (d) Calculate the area under the curve...
1 Expectation, Co-variance and Independence [25pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is 0.5 x=1 0.5 x=-1 Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y are independent. Meanwhile, let Z = XY. N(0,1). X and Y (a) What is the Expectation (mean value) of X? 3pts (b) Are Y and Z independent? (Just clarify, do not need to prove) [2pts c)...
5. Determine the characteristic function Ø(u) = E(exp(ju? x)] of the Gaussian random vector X having mean m= [1 3]T and covariance matrix C = [? 2]
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
1. Consider the transformed function g(x)=-3 +2 of the function (x Then answer the following: a. List the sequence of transformations in a correct order. b. Write the equation of the horizontal asymptote. c. Find the vertical intercept of g(x) written as an ordered pair. d. Find the horizontal intercept algebraically and leave it in an exact form (not decimal approximation). e. Sketch the graph of g(x) 2. Solve the following equations algebraically for x : a. 16-) = 82-1...
Previous Problem Results for this submission Entered (e^x)"I((e^x)+2)*(x+1)^(-2)]*[x*(e^e)+2] -e/((ez The answer above is NOT correct. (1 point) Calculate the derivative using the appropriate rule or combination of rules. (ex + 2)(2+1) f'(x)= (-eº X (e^x+2)(X+1)) -2)*(xe°e+2). Preview My Answers Submit Answers Your score was recorded You have attempted this problem 10 times att earch
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