e^x maclaurin serie

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Firuze
Firuze 2024-1-15
编辑： owen 2024-9-16
Hello everyone, I'm very new to MATLAB. Could you help me with this question please?
How to write codes that calculate e^x by serializing the x value entered from the keyboard into a series equal to the number of terms (N) entered from the keyboard?
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Sam Chak
Sam Chak 2024-1-15
Ran in:
Hi @Firuze,
I realized that I can use the taylor() function to compute the Maclaurin series without having to memorize the series expansion. There are several solutions, depending on whether certain built-in functions can be used or not in your homework.
%% Get input values from the Keyboard User
% x = input('Enter the value of x: ');
% N = input('Enter the number of terms (N): ');
x = 1;
N = 5;
sympref('PolynomialDisplayStyle', 'ascend');
syms x
%% Display the series expansion for e^x
T = taylor(exp(x), x, 'Order', N+1) % Unsure how you define the number of terms
T = 
%% Evaluate the series
Teval = double(subs(T, x, 1))
Teval = 2.7167

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Hassaan
Hassaan 2024-1-15
编辑：Hassaan 2024-1-15
@Firuze
Numerically:
% Prompt the user to enter the value of x
x = input('Enter the value of x: ');
% Prompt the user to enter the number of terms N
N = input('Enter the number of terms N: ');
% Initialize the result of e^x
ex = 1; % The first term of the series is always 1
% Calculate e^x using the series expansion [for-loop]
for n = 1:N
term = x^n / factorial(n); % Calculate each term in the series
ex = ex + term; % Add each term to the result
end
% % Calculate e^x using the series expansion [vectorization]
% n = 0:N;
% ex = sum(x.^n ./ factorial(n));
% Display the result
fprintf('e^x calculated using the series expansion is: %f\n', ex);
% For comparison, calculate e^x using MATLAB's exp function
ex_true = exp(x);
fprintf('e^x calculated using MATLAB''s exp function is: %f\n', ex_true);
It will prompt you to input the value of x and the number of terms N. Then, it will calculate and display the result of e^x using the series expansion up to N terms. Additionally, it shows the result calculated by MATLAB's built-in exp function for comparison.
Output
Enter the value of x: 1
Enter the number of terms N: 5
e^x calculated using the series expansion is: 2.716667
e^x calculated using MATLAB's exp function is: 2.718282
Symbol Evaluation
% Ask for input from the keyboard
x = input('Enter the value of x: ');
N = input('Enter the number of terms N: ');
% Initialize the symbolic variable and the result
syms n;
ex = sym(0); % Symbolic 0
% Calculate the series expansion symbolically
for n = 0:N-1
ex = ex + (x^n)/factorial(n);
end
% Display the symbolic result
disp(ex);
Symbolic Expression
% Define the symbolic variable x and the summation index n
syms x n;
% Ask for input for the number of terms in the series N
N = input('Enter the number of terms N: ');
% Define the symbolic expression for the series expansion of e^x
e_x_series = symsum(x^n/factorial(n), n, 0, N-1);
disp(e_x_series)
% Pretty print the symbolic series expansion
% pretty(e_x_series)
Output
Enter the number of terms N: 5
x^4/24 + x^3/6 + x^2/2 + x + 1
------------------------------------------------------------------------------------------------------------------------------------------------
If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.
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John D'Errico
John D'Errico 2024-1-15
Please do not do obvious homework assignments for students who show no effort. This does not help the student. It teaches them only that there is always some sucker willing to do their homework for them.
Worse, it teaches that same student to then keep on posting additional homework assignments, thinking they have landed on a homework gold mine.
And finally, it teaches other students to follow their lead. This damages the forum itslef, as we will be overwhelmed with students posting their homework.
Hassaan
Hassaan 2024-1-15
编辑：Hassaan 2024-1-15
@John D'Errico I do agree and I try to avoid as much as possible such scenarios.

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更多回答（1 个）

Sulaymon Eshkabilov
编辑：Sulaymon Eshkabilov 2024-1-15
A function can be written to compute Mclaurin series approximation, e.g.:
% E.g.: approximation of exp(x) at x = pi
x = pi;
N_terms = 10; % Number of terms in the series
Solution = Maclaurin(x, N_terms);
fprintf('Maclaurin series approx. for exp(%g) with %d terms: %g\n', x, N_terms, Solution);
function function SOL = Maclaurin(x, terms)
n = 0:terms;
SOL = sum((x.^n) ./ factorial(n));
end
Alt. Solution (computationally slow)
% E.g.: approximation of exp(x) at x = pi
x = pi;
N_terms = 10; % Number of terms in the series
Solution = Maclaurin2(x, N_terms);
fprintf('Maclaurin series approx. for exp(%g) with %d terms: %g\n', x, N_terms, Solution);
function SOL = Maclaurin2(x, terms)
SOL = 1; % Initialize with the first term
for n = 1:terms
SOL = SOL + x^n / factorial(n);
end
end
  2 个评论
John D'Errico
John D'Errico 2024-1-15
Please do not do obvious homework assignments for students who show no effort. This does not help the student. It teaches them only that there is always some sucker willing to do their homework for them.
Worse, it teaches that same student to then keep on posting additional homework assignments, thinking they have landed on a homework gold mine.
And finally, it teaches other students to follow their lead. This damages the forum itslef, as we will be overwhelmed with students posting their homework.
owen
owen 2024-9-16
编辑：owen 2024-9-16
I am trying to do the same series but not with e^x, i tried looking into to code but i am a bit confused where i put the equation and how i change the e^x into the function i want. Could someone please help me with that?

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