Differentiate the following function: f(x) = ex -2x +1
Matlab
MECE 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.
Homework Answers
#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. Find the first derivative of a functionf(x)-ex (a) Use calculus to determine the correct value...
3. Find the first derivative of a functionf(x)-ex (a) Use calculus to determine the correct value of the derivative at x = 2. If h = 0.25, (b) Evaluate the second-order centered finite-difference approximation (e) Evaluate the second-order forward difference approximation. (d) Evaluate the second-order backward difference approximation. (e) Create a MATLAB function program, which gives output up to second order centered finite difference approximation of second derivative "(xo). The input arguments aref n (order of approximation, 1 or 2),...
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
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and...
please show the matlab coding
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.
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...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The ...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
5. Create a MATLAB script to find the first and second derivative of given function using Forward, Backward, central an...
5. Create a MATLAB script to find the first and second derivative of given function using Forward, Backward, central and Taylor numerical schemes. Test your code using the following functions: f(x)-xe*+3x2 +2x -1 and find f (3) and f' (3) for with h 0.1, 0.01 and 0.001 b. Approximate y'(1) and y"(1) using the following table f(x) 0.992 0.8 0.9 0.999 1.0 1.001 1.008 Input: (copy and paste the MATLAB or Scilab script in the following box)
5. Create a...
Example 1 Find the first derivative of the function below analytically and with forward, backward and...
Example 1 Find the first derivative of the function below analytically and with forward, backward and centered difference formulas at x = 0.5 and Ax=0.1. Find the true errors. f(x) = cos(3x)
Use Microsoft excel to estimate the derivative of the following function: Please answer all questions. Use Microsoft Excel to estimate the derivative of the following functionc Note that the anal...
Use
Microsoft excel to estimate the derivative of the following
function:
Please answer all questions.
Use Microsoft Excel to estimate the derivative of the following functionc Note that the analytical derivative is fo- 3x-2x-3. Generate a table of ordered values for the function its analytical derivati e and an mencal estimate of the derivatwe. Use the first orde, centered method to esti ate the dem ative at x two digits to the right of the decimal place in your answer....
#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. Find the first derivative of a functionf(x)-ex (a) Use calculus to determine the correct value of the derivative at x = 2. If h = 0.25, (b) Evaluate the second-order centered finite-difference approximation (e) Evaluate the second-order forward difference approximation. (d) Evaluate the second-order backward difference approximation. (e) Create a MATLAB function program, which gives output up to second order centered finite difference approximation of second derivative "(xo). The input arguments aref n (order of approximation, 1 or 2),...
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
please show the matlab coding
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.
Exercise 4. Calculate the derivative of j(r) = besselj (1,x) at x = 1 using forward, backward and centered finite differences with a step h = 0.1.
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
5. Create a MATLAB script to find the first and second derivative of given function using Forward, Backward, central and Taylor numerical schemes. Test your code using the following functions: f(x)-xe*+3x2 +2x -1 and find f (3) and f' (3) for with h 0.1, 0.01 and 0.001 b. Approximate y'(1) and y"(1) using the following table f(x) 0.992 0.8 0.9 0.999 1.0 1.001 1.008 Input: (copy and paste the MATLAB or Scilab script in the following box)
5. Create a...
Example 1 Find the first derivative of the function below analytically and with forward, backward and centered difference formulas at x = 0.5 and Ax=0.1. Find the true errors. f(x) = cos(3x)
Use
Microsoft excel to estimate the derivative of the following
function:
Please answer all questions.
Use Microsoft Excel to estimate the derivative of the following functionc Note that the analytical derivative is fo- 3x-2x-3. Generate a table of ordered values for the function its analytical derivati e and an mencal estimate of the derivatwe. Use the first orde, centered method to esti ate the dem ative at x two digits to the right of the decimal place in your answer....
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