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riva February 2016
### Taylor series approximation when the series is truncated after the ﬁrst, second and third term, in MATLAB

I want to write an m-ﬁle `function demoTaylorlog(x0,dx)`

that does the equivalent but for the Taylor series representation of `f(x) = ln(x)`

.
This is what I have, but it does not work. I am not sure if it is the right code. How should I fix it?

```
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
```

In the statement `f(x)= log(x);`

`f`

is a vector and `log`

is a function. Suppose that your `x`

vector is `[0.12 0.24 0.36]`

then the statement with the error is equivalent to:

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

But if `f`

is a vector the assignment to `f(0.12)`

has no sense because .12 is not a positive integer or a logical value (as the error says).

You should write `f = log(x);`

Asked in February 2016

Viewed 1,017 times

Voted 12

Answered 1 times

Viewed 1,017 times

Voted 12

Answered 1 times