Homework Answers
Matlab code for the problem
clc; clear; % clearing the command window and workspace
% the 7th degree polymonial as matlab anonymous function
sine = @(x)
x-x.^3/factorial(3)+x.^5./factorial(5)-x.^7./factorial(7);
x = [0 3*pi/2]; % x range
y = [-1.5 2]; % y range
fplot(@(x) sin(x),x,'b'); % plotting matlab sine function for
x
hold on % hold the plot
fplot(sine,x,'r--'); % plotting the polynomial approximation of
sine
axis tight
figure % next figure for y domain
fplot(@(x) sin(x),y,'b'); % plotting matlab sine function for
y
hold on % holding the figure
fplot(sine,y,'r--'); % plotting the polynomial function for y
axis tight
Screen Print of the code
Screen Print of the output
Add Answer to:
8. The Maclaurin series (a special case of the Taylor series that is discussed later in...
This is the given code: /** * This program uses a Taylor Series to compute a...
This is the given code:
/**
* This program uses a Taylor Series to compute a value
* of sine.
*
*/
#include<stdlib.h>
#include<stdio.h>
#include<math.h>
/**
* A function to compute the factorial function, n!.
*/
long factorial(int n) {
long result = 1, i;
for(i=2; i<=n; i++) {
result *= i;
}
return result;
}
int main(int argc, char **argv) {
if(argc != 3) {
fprintf(stderr, "Usage: %s x n ", argv[0]);
exit(1);
}
double x = atof(argv[1]);
int...
5,9,13,17 1-X 1. What is the difference between a Taylor series and Maclaurin series? 2. T/F:...
5,9,13,17
1-X 1. What is the difference between a Taylor series and Maclaurin series? 2. T/F: In general, pn() approximates f(x) better and better as n gets larger. 3. For some function f(x), the Maclaurin polynomial of degree 4 is pa(x) = 6 + 3x - 4x + 5x – 7x*. What is p2(x)? 4. For some function f(x), the Maclaurin polynomial of degree 4 is p(x) = 6 + 3x - 4x + 5x – 7x*. What is f"O)?...
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approx...
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f (x) T (x) when x lies in the interval 0.5 rs 1.5 17. Find the first three nonzero terms in the Maclaurin series for the function f (x) = --_" and (r+3) its radius of convergence.
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f...
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f an...
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Convince yourself that the Maclaurin Series for cos(x) is: A. Write a function script called cos...
Convince yourself that the Maclaurin Series for cos(x) is:
A. Write a function script called cos_series
that takes that takes as its inputs, x and N and has output given
by the sum in the N-term Maclaurin Series approximation for Cos(x).
Hint: try a “for loop” and set “format long” in
your code. You may use the MATLAB built-in function factorial()
B. Check your code by finding the 2-terms,
3-terms, 4-terms, 5-terms and 6-terms Maclaurin Series
approximations every 30 degrees...
An alternative way for calculating sin(x) is to use its Taylor series as the following: sinx)x-+...
An alternative way for calculating sin(x) is to use its Taylor series as the following: sinx)x-+ Create a function named "sin_taylor" in MATLAB. This function takes two inputs. First input is the angle, and the second input determines the number of terms in Taylor series for approximation. Check the fidelity of your function by running sin-taylor( 7) and compare it with the exact value of it. Hint: “factorial" is a built-in function that you can use for calculating factorial of...
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the...
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the following function: f(x) = (-3x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.3. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fittin...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fitting higher and higher degree polynomials T, a(x) to the curve at the point (a, f(a)), with the goal of getting a better and better fit as we not only let the degree grow larger, but take a series whose partial sums are these so-called Taylor polynomials Tm,a(x) We will explore how this is done by determine the Taylor series of f(z)...
Problem 1 MATLAB A Taylor series is a series expansion of a function f()about a given point a. For one-dimensional real...
Problem 1 MATLAB
A Taylor series is a series expansion of a function f()about a given point a. For one-dimensional real-valued functions, the general formula for a Taylor series is given as ia) (a) (z- a) (z- a)2 + £(a (r- a) + + -a + f(x)(a) (1) A special case of the Taylor series (known as the Maclaurin series) exists when a- 0. The Maclaurin series expansions for four commonly used functions in science and engineering are: sin(x) (-1)"...
dont ans this question Euler's method is based on the fact that the tangent line gives...
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
This is the given code:
/**
* This program uses a Taylor Series to compute a value
* of sine.
*
*/
#include<stdlib.h>
#include<stdio.h>
#include<math.h>
/**
* A function to compute the factorial function, n!.
*/
long factorial(int n) {
long result = 1, i;
for(i=2; i<=n; i++) {
result *= i;
}
return result;
}
int main(int argc, char **argv) {
if(argc != 3) {
fprintf(stderr, "Usage: %s x n ", argv[0]);
exit(1);
}
double x = atof(argv[1]);
int...
5,9,13,17
1-X 1. What is the difference between a Taylor series and Maclaurin series? 2. T/F: In general, pn() approximates f(x) better and better as n gets larger. 3. For some function f(x), the Maclaurin polynomial of degree 4 is pa(x) = 6 + 3x - 4x + 5x – 7x*. What is p2(x)? 4. For some function f(x), the Maclaurin polynomial of degree 4 is p(x) = 6 + 3x - 4x + 5x – 7x*. What is f"O)?...
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f (x) T (x) when x lies in the interval 0.5 rs 1.5 17. Find the first three nonzero terms in the Maclaurin series for the function f (x) = --_" and (r+3) its radius of convergence.
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f...
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Convince yourself that the Maclaurin Series for cos(x) is:
A. Write a function script called cos_series
that takes that takes as its inputs, x and N and has output given
by the sum in the N-term Maclaurin Series approximation for Cos(x).
Hint: try a “for loop” and set “format long” in
your code. You may use the MATLAB built-in function factorial()
B. Check your code by finding the 2-terms,
3-terms, 4-terms, 5-terms and 6-terms Maclaurin Series
approximations every 30 degrees...
An alternative way for calculating sin(x) is to use its Taylor series as the following: sinx)x-+ Create a function named "sin_taylor" in MATLAB. This function takes two inputs. First input is the angle, and the second input determines the number of terms in Taylor series for approximation. Check the fidelity of your function by running sin-taylor( 7) and compare it with the exact value of it. Hint: “factorial" is a built-in function that you can use for calculating factorial of...
Question 4: Talyor. Maclaurin and Power Series For parts a, b, c and d, use the following function: f(x) = (-3x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.3. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fitting higher and higher degree polynomials T, a(x) to the curve at the point (a, f(a)), with the goal of getting a better and better fit as we not only let the degree grow larger, but take a series whose partial sums are these so-called Taylor polynomials Tm,a(x) We will explore how this is done by determine the Taylor series of f(z)...
Problem 1 MATLAB
A Taylor series is a series expansion of a function f()about a given point a. For one-dimensional real-valued functions, the general formula for a Taylor series is given as ia) (a) (z- a) (z- a)2 + £(a (r- a) + + -a + f(x)(a) (1) A special case of the Taylor series (known as the Maclaurin series) exists when a- 0. The Maclaurin series expansions for four commonly used functions in science and engineering are: sin(x) (-1)"...
dont ans this question
Euler's method is based on the fact that the tangent line gives a good local approximation for the function. But why restrict ourselves to linear approximants when higher degree polynomial approximants are available? For example, we can use the Taylor polynomial of degree about = No, which is defined by P.(x) = y(x) + y (xo)(x – Xa) + 21 (x- This polynomial is the nth partial sum of the Taylor series representation (te) (x –...
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