Question

我想编写一个m-fi文件function demoTaylorlog(x0,dx)来完成等效但是f(x) = ln(x)的泰勒系列表示。这就是我所拥有的，但它不起作用。我不确定它是否是正确的代码。我该如何解决？

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

在声明中f(x)= log(x); f是一个向量，log是一个函数。假设您的x向量为[0.12 0.24 0.36]，则带有错误的语句相当于：

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

但如果f是向量，则f(0.12)的赋值没有意义，因为.12不是正整数或逻辑值（如错误所示）。

你应该写f = log(x);

在MATLAB中，在第一，第二和第三项之后截断系列时的泰勒级数近似

1 个答案: