Homework Answers
Add Answer to:
Problem 1 Consider the function f(x) x3 +3/x. Calculate the first derivative with respect to x...
3. A five-point centered finite difference approximation to the first derivative is given by - f...
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
4. The first derivative of a function f(x) at a point x = xo can be approximated with the four-po...
Solve using MATLAB and provide code please
4. The first derivative of a function f(x) at a point x = xo can be approximated with the four-point central difference formula: dx 12h where h is a small number relative to xo. Write a user-defined function function that calculates the derivative of a math function fx) by using the four-point central difference formula. For the user-defined function name, use dfax-FoPrder(Fun, x0), where Fun is a name for the function that is...
For the following Integration: F(x) = x3 – x dx where: n = 8 (# of...
For the following Integration: F(x) = x3 – x dx where: n = 8 (# of pieces) a- Calculate the exact solution for the given integration by using Traditional methods. b- Estimate the integration numerically by using Trapezoid rule and calculate the error. C- Estimate the integration numerically by using Simpson rule and calculate the error.
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx...
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx 0 using O(h) finite difference (forward and backward) and O(h2) centered finite difference. Vary h in the following manner: 1, 101,102... 1015. (Write a MATLAB script for this purpose and call it pset5_prob7) (b) Modify your script to plot (log-log) the the true percent error in all three cases as a function of h in one plot. (c) In calculus we learned that...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a)...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a) Obtain the analytical expression (i.e. True or Exact Solution) for the first derivative, Eval- uate its value at 1 =0.5. Box your answer and label it as fexact- (b) Now assume the function is discretized on a grid with uniform spacing of h. Evaluate your finite difference approximation at x = 0.5 using central differencing with step sizes starting at 1 and re- duced...
Differentiate the following function: f(x) = ex -2x +1
MatlabMECE 2350 Numerical Methods Lab 8.1. Differentiate the following function: f(x) = ex -2x +1 and solve its first derivative atx = 8 2. Numerically evaluate the approximated first derivative from the above function at x = 8 and h = 0.15 by the following: (a) Forward finite difference method (b) Backward finite difference method (c) Centered finite difference method 3. Calculate the error of each method by comparing the numerical derivative with the result from problem 1.
MATLAB 1) Calculate the following for the function f(x) = e-4x- 2x3
#use MATLAB script1) Calculate the following for the function f(x) = e-4x- 2x3 a. Calculate the derivative of the function by hand. Write a MATLAB function that calculates the derivative 05. of this function and calculate the derivative at x = 0.5. b. Develop an M- to evaluate the cetered finite-difference approximation (use equation below), at x = 0.5. Assume that h = 0.1. c. Repeat part (b) for the second-order forward and backward differences. Again Assume that h = 0.1. d. Using the results...
Please help me answer this question using matlab Consider the function f(x) x3 2x4 on the...
Please help me answer this question using matlab
Consider the function f(x) x3 2x4 on the interval [-2, 2] with h 0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate a...
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate af/az. Э//ду, and Эг f/0гду) at x = y = 1 numerically using 2nd-order central difference formula with a grid spacing h -0.1. Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework...
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) a...
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error) of the numerical approximation of the derivative in each case.
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error)...
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
Solve using MATLAB and provide code please
4. The first derivative of a function f(x) at a point x = xo can be approximated with the four-point central difference formula: dx 12h where h is a small number relative to xo. Write a user-defined function function that calculates the derivative of a math function fx) by using the four-point central difference formula. For the user-defined function name, use dfax-FoPrder(Fun, x0), where Fun is a name for the function that is...
For the following Integration: F(x) = x3 – x dx where: n = 8 (# of pieces) a- Calculate the exact solution for the given integration by using Traditional methods. b- Estimate the integration numerically by using Trapezoid rule and calculate the error. C- Estimate the integration numerically by using Simpson rule and calculate the error.
#7. [Extra Credit] is calculus wrong?! Consider f(x) = ex (a) Calculate the derivative of fx) atx 0 using O(h) finite difference (forward and backward) and O(h2) centered finite difference. Vary h in the following manner: 1, 101,102... 1015. (Write a MATLAB script for this purpose and call it pset5_prob7) (b) Modify your script to plot (log-log) the the true percent error in all three cases as a function of h in one plot. (c) In calculus we learned that...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a) Obtain the analytical expression (i.e. True or Exact Solution) for the first derivative, Eval- uate its value at 1 =0.5. Box your answer and label it as fexact- (b) Now assume the function is discretized on a grid with uniform spacing of h. Evaluate your finite difference approximation at x = 0.5 using central differencing with step sizes starting at 1 and re- duced...
Please help me answer this question using matlab
Consider the function f(x) x3 2x4 on the interval [-2, 2] with h 0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivatives so as to graphically illustrate which approximation is most accurate. Graph all three first-derivative finite difference approximations along with the theoretical, and do the same for the second derivative as well
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate af/az. Э//ду, and Эг f/0гду) at x = y = 1 numerically using 2nd-order central difference formula with a grid spacing h -0.1. Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework...
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error) of the numerical approximation of the derivative in each case.
1. U se Taylors formula to derive the forward, backward and center difference for- mulas for the derivative /"(x) at a point x Use the reminder in Taylors formula to determine the order (truncation error)...
Most questions answered within 3 hours.
-
Write the ionic equations for the first stage of salts
hydrolysis.
Anion, Cation?
Na2S
NiSO4
K2SO4...
asked 39 minutes ago -
suppose there is a normally distributed population with a mean of
250 and a standard deviation...
asked 1 hour ago -
Question Three
Suppose you as project manager are using the Waterfall
development methodology on a large...
asked 2 hours ago -
Which statement is not true about welfare in Canada?
A.Benefits typically vary based on one's ability...
asked 2 hours ago -
Please help me with FLOWCHART and UML diagram for class,
thank you!
#include <iostream>
#include <fstream>...
asked 3 hours ago -
3. Describe the “logic circuit” of the Lac operon. Which
proteins are bound or not to...
asked 3 hours ago -
Ayesha’s adjusted gross income is $60,000 in 2019. She donated a
piece of artwork with a...
asked 3 hours ago -
For Dijkstra’s shortest path algorithm:
a. Give the Big-O time for Dijkstra’s shortest path algorithm
and...
asked 3 hours ago -
Phosphorus violates the 'octet rule' in biological molecules,
forming more covalent bonds than expected based on...
asked 4 hours ago -
A 1.3 eV electron has a 10-4 probability of tunneling
through a 2.4 eV potential barrier....
asked 4 hours ago -
What is the one ingredient that is common to being successful
with all stakeholders?
profit
trust...
asked 4 hours ago -
Write an assembly language 32 bit program that reads in lines of
text by a .txt...
asked 4 hours ago