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6. If < 1, it is known that Write a function seriesapprox to perform the following...
4.2 The Maclaurin series expansion for cos x is 6 .8 Starting with the simplest version,...
4.2 The Maclaurin series expansion for cos x is 6 .8 Starting with the simplest version, cos -I, add terms one at a time to estimate cos(π/3). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error crite- rion conforming to two significant figures.
Create a MATLAB function to perform Lagrange Interpolation. Your function will be used as illustrated below:...
Create a MATLAB function to perform Lagrange Interpolation. Your function will be used as illustrated below: >> ya = Lagrange(x, y, a) where "x" is a vector of ? independent data values, "y" is a vector of ? dependent function values corresponding to "x", "a" is an arbitrary value of "x" for which you want to know the Westimate of "y", and "ya" is the estimate of the function at x=a. Print an error message and exit the function if...
Consider the function /(x) = -3x - 2x2, the true value of its root is x*...
Consider the function /(x) = -3x - 2x2, the true value of its root is x* -0.392474. (1) Use the Newton-Raphson Method starting with x = 0, the new approximation to the root after one iteration is .x2 = __ __blank The true absolute error is EP =____blank 2__ (2) The new approximation to the root after one more iteration is x3 = ___ _blank 3 Use six significant digits for x; to calculate the true absolute error E -_...
1. For the series below, use Excel to generate a table with columns of absolute true...
1. For the series below, use Excel to generate a table with columns of absolute true error, absolute approximate error, absolute percent relative true error, and absolute percent relative approximate error and plots of absolute percent true error and absolute percent approximate error vs number of terms calculated for x - 0.75. Calculate up to 10 terms. Use Excel's Inx function to generate a true value.
Submission Items: (1) A Word document in which you: a. Describe in brief the problem you...
Submission Items: (1) A Word document in which you: a. Describe in brief the problem you are solving and the numerical method used. b. Snapshot of the output, when you run the program for the conditions mentioned in the questions. c. Discuss your results. (2) MATLAB code (m) file() Question 1: [10 points) Write a MATLAB function that calculates the approximate value of arctan(x) using the Maclaurin series approximation: arctan(x) = x- + +... The function should accept 3 parameters:...
MATLAB ONLY!! PLEASE WRITE IN COMPUTER SO I CAN COPY PASTE!!! ANSWER COMPLETELY, USE FOR LOOPS....
MATLAB ONLY!! PLEASE WRITE IN COMPUTER SO I CAN COPY
PASTE!!! ANSWER COMPLETELY, USE FOR LOOPS.
THE PROGRAM TO BE MODIFIED IS THE NEXT ONE:
clc
clear
% Approximate the value of e ^ x using the Taylor Series
x = input( 'Enter the value of x for e^x. x = ' );
t = input( 'Enter the amount of desired terms. t = ' );
i = 1;
e_taylor = 0; % initializing the variable for the
accumulator
while...
someone please do this corrcetly using matlab and following all instructions 1. (30 Points) It is...
someone please do this corrcetly using matlab and following
all instructions
1. (30 Points) It is known that the sine function can be expressed as: x(2k+1) sin(x) = (-1) +(2k + 1)! k=0 Truncate the series to compute the first seven estimates (ie, for k = 0,1,2,3,4,5, and 6) for x = You must use a for loop. All calculations and printing the table described below should be done from within the loop. For each estimate, determine the magnitude of...
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...
please show me a Matlab script that will compute the total errors of the approximation due...
please show me a Matlab script that will compute the
total errors of the approximation due to the given function, also
include the panel plot as well, thank you.
1) This problem studies the errors due to the approximation of the first derivative of a given function f(x) using the forward and centered difference methods. For this problem, we consider f(x)=sin(x). a) First, we will investigate the effect of the step size h on the first derivative approximation. Set h=10',...
Implement MATLAB code that calculates sin(x) using the following formula, and measure the absolute error from...
Implement MATLAB code that calculates sin(x) using the following formula, and measure the absolute error from the MATLAB provided function. The Taylor's formula is given as follows: sin(x) = 0+12 + 0x² + 5123 + 0.x4 + ... 23 25 27 -3! + 5- 7 + ... Plot both (1) the approximated value, and (2) absolute error. The following example uses x = 3 * pi, and k = 50. You may choose your own x, and k values. Approximation:...
4.2 The Maclaurin series expansion for cos x is 6 .8 Starting with the simplest version, cos -I, add terms one at a time to estimate cos(π/3). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error crite- rion conforming to two significant figures.
Consider the function /(x) = -3x - 2x2, the true value of its root is x* -0.392474. (1) Use the Newton-Raphson Method starting with x = 0, the new approximation to the root after one iteration is .x2 = __ __blank The true absolute error is EP =____blank 2__ (2) The new approximation to the root after one more iteration is x3 = ___ _blank 3 Use six significant digits for x; to calculate the true absolute error E -_...
1. For the series below, use Excel to generate a table with columns of absolute true error, absolute approximate error, absolute percent relative true error, and absolute percent relative approximate error and plots of absolute percent true error and absolute percent approximate error vs number of terms calculated for x - 0.75. Calculate up to 10 terms. Use Excel's Inx function to generate a true value.
Submission Items: (1) A Word document in which you: a. Describe in brief the problem you are solving and the numerical method used. b. Snapshot of the output, when you run the program for the conditions mentioned in the questions. c. Discuss your results. (2) MATLAB code (m) file() Question 1: [10 points) Write a MATLAB function that calculates the approximate value of arctan(x) using the Maclaurin series approximation: arctan(x) = x- + +... The function should accept 3 parameters:...
MATLAB ONLY!! PLEASE WRITE IN COMPUTER SO I CAN COPY
PASTE!!! ANSWER COMPLETELY, USE FOR LOOPS.
THE PROGRAM TO BE MODIFIED IS THE NEXT ONE:
clc
clear
% Approximate the value of e ^ x using the Taylor Series
x = input( 'Enter the value of x for e^x. x = ' );
t = input( 'Enter the amount of desired terms. t = ' );
i = 1;
e_taylor = 0; % initializing the variable for the
accumulator
while...
someone please do this corrcetly using matlab and following
all instructions
1. (30 Points) It is known that the sine function can be expressed as: x(2k+1) sin(x) = (-1) +(2k + 1)! k=0 Truncate the series to compute the first seven estimates (ie, for k = 0,1,2,3,4,5, and 6) for x = You must use a for loop. All calculations and printing the table described below should be done from within the loop. For each estimate, determine the magnitude of...
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 show me a Matlab script that will compute the
total errors of the approximation due to the given function, also
include the panel plot as well, thank you.
1) This problem studies the errors due to the approximation of the first derivative of a given function f(x) using the forward and centered difference methods. For this problem, we consider f(x)=sin(x). a) First, we will investigate the effect of the step size h on the first derivative approximation. Set h=10',...
Implement MATLAB code that calculates sin(x) using the following formula, and measure the absolute error from the MATLAB provided function. The Taylor's formula is given as follows: sin(x) = 0+12 + 0x² + 5123 + 0.x4 + ... 23 25 27 -3! + 5- 7 + ... Plot both (1) the approximated value, and (2) absolute error. The following example uses x = 3 * pi, and k = 50. You may choose your own x, and k values. Approximation:...
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