How do I write the function to derive an nth taylor polynomial?

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James T 2017-9-12

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评论： James T 2017-9-13

function y = nthTaylorPolyExp( n, x )
%y = nthTaylorPolyExp( n, x )is a function that returns 3rd Taylor polynomial of exponential function at x=0.
%       n is an input argument, which indicates the degree of Taylor
%           polynomial.
%       x is an input argument
%       y is output.
y=zeros('like',x);
% ============= YOUR CODE HERE ==============
% Instructions: Return nth Taylor polynomial of exponential function at x=0.
%               You can use built in function factorial(n) to return n!,
%               and use for loop to get the sum.
for i = 0:n
      % y = y + (-1)^i * (x.^(2 * i)) / factorial(2 * i); is my version, but its incorrect.
end
% ===========================================
end

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Answer 1

James Tursa 2017-9-12

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https://ww2.mathworks.cn/matlabcentral/answers/356352-how-do-i-write-the-function-to-derive-an-nth-taylor-polynomial#answer_281294

You are using the series expansion for cos( ), not the series expansion for exp( ). You need to replace the terms you are using with the terms that match the series expansion for exp( ).