write taylor series of log x with base point 1 manually in matlab

To manually write the Taylor series of log(x) with base point 1 in MATLAB, we need to find the derivatives and evaluate them at x=1. The Taylor series of log(x) with base point 1 can be written as:

main.m
log(x) = (x-1) - (x-1)^2/2 + (x-1)^3/3 - (x-1)^4/4 + ...
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Here is a MATLAB code snippet that calculates the Taylor series expansion of log(x) with base point 1:

main.m
x = sym('x');
f = log(x);  % the function we want to expand
a = 1;  % base point for the expansion
n = 5;  % number of terms in the Taylor series

taylor_series = sym(zeros(1, n));
taylor_series(1) = f;
for i = 2:n
    taylor_series(i) = subs(diff(taylor_series(i-1)), x, a)*(x-a)/i;
end

taylor_series_expansion = simplify(sum(taylor_series));
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In this code, we first define the symbolic variable x and the function f as log(x). The base point for the expansion is a = 1, and n is the number of terms we want in the Taylor series.

We then initialize an array taylor_series to store each term in the series. The first term is set as the original function f. We then use a loop to calculate each subsequent term using the formula for the derivative at the base point a and multiplying it by (x-a)/i to account for the correct power of (x-a). The diff function is used to calculate the derivative.

Finally, we use the sum function to add up all the terms in the taylor_series array, and the simplify function to simplify the resulting expression.

You can modify the value of n to get more terms in the Taylor series expansion.

Note that using the symbolic toolbox (sym) allows us to work with symbolic expressions and perform exact calculations.