泰勒級數近似當系列在第一，第二和第三項之後被截斷時，在MATLAB中

Question

我想寫一個等效的模擬文件function demoTaylorlog(x0,dx)，但是對於泰勒級數表示f(x) = ln(x)。 這是我的，但它不起作用。我不確定它是否是正確的代碼。我應該如何解決它？

function demoTaylorlog(x0,dx) 

% demoTaylor Taylor Series approximations for f(x) = 1/(1-x) 
%Synopsis: 
%  demoTaylorlog(x0,dx) 
% Input: x0 = (optional) point about which the Taylor Series expansion is 
%    made. Default: x0 = 1.6; 
%   dx = (optional) size of neighborhood over which the expansion 
%    is evaluated. Default: dx = 0.8 
% Output: a plot of f(x) and its Taylor Series approximations 

if nargin<2, x0 = 1.6; dx = 0.8; end 

x = linspace(x0-dx/2,x0+dx/2,20); 
% x-values at which f(x) is evaluated  
f(x)= log(x);      
% Exact f(x); notice the array operator 
h = x - x0;      
% Avoid recomputing intermediate values, 
t = 1/(1-x0);      
% h and t p1x = t*ones(size(x)) + h*t^2; 
% First order Taylor polynomial p2x = p1x+ (h.^2)*t^3;   
% Second order " " " p3x = p2x + (h.^3)*t^4;   
% Third 
plot(x,fx,'-',x,p1x,'o-',x,p2x,'^-',x,p3x,'s-'); 
legend('exact','P_1(x)','P_2(x)','P_3(x)',4); 
xlabel('x');  
ylabel('Approximations to f(x) = 1/(1-x)'); 

end 

Answer 1

在聲明f(x)= log(x);f是一個向量和log是一個函數。假設你x矢量[0.12 0.24 0.36]然後用錯誤的語句等價於：

f(0.12) = log(0.12); 
f(0.24) = log(0.24); 
f(0.36) = log(0.36); 

但如果f是一個矢量分配給f(0.12)已經沒有意義，因爲1.12處於不是正整數或邏輯值（如錯誤所述）。

你應該寫f = log(x);