By using syntax ‘taylor’ in MATLAB, find the third order approximation of log x using base point at x = 1.

syms x
f = logx;
T = taylor(f, 'Order', 3)

Undefined function or variable 'logx'.

How can i do that above question? I have tried but i was unable to generate

[Walter Roberson]

There is no logx function. The available logarithmetic functions are log, log2, and log10

[melissa tan]

Then how do i do the above question . I am a bit confused. Actually i have read the taylor document , but i don't understand that why i am asking here . Thank you.

[melissa tan]

>> syms x taylor(log(x),x,'order',3) Error using symengine Unable to compute a Taylor expansion.

Error in sym/taylor (line 128) tSym = mupadmex('symobj::taylor',f.s,x.s,a.s,options);

Is it like this to solve this question but why is there error?

[Walter Roberson]

The default expansion point is 0, but diff(log(x)) is infinite at 0. You need a nonzero expansion point.

[melissa tan]

How do i set nonzero expanision point?

[melissa tan]

taylor(log(x),x,1,'order',3)

ans =

x - (x - 1)^2/2 - 1

[melissa tan]

is the solution for the above question correct? i have spent 1 h to figure out. Thank you.

[Torsten]

Usually, the order of a Taylor series means the order of the approximating polynomial for the function in question. In Matlab, 'Order' means the exponent in the O-term. Thus I suspect that you will have to choose 'Order' in the Taylor command to be 4 instead of 3:

syms x
f = log(x);
p = taylor(f,x,'ExpansionPoint',1,'Order',4)

Best wishes

Torsten.

[melissa tan]

is the expansion point means the give point of my question which x=1?

[Torsten]

Yes.

But why don't you read the documentation:

https://de.mathworks.com/help/symbolic/taylor.html

?

Your question is almost answered in the section "Specify Expansion Point".

Best wishes

Torsten.

[melissa tan]

I have read it but i don't really understand. Thank you so much .

Answer 1

[Dongji Lee]

Or you can type it in simple manner.

T = taylor(f,x,1,'Order', 3)

Answer 2

[John D'Errico]

Hint: MATLAB does not know that when you type logx, in fact you wanted it to compute the function log(x). As well, you need to understand that a Taylor series of log(x) around the default expansion point of x==0 will be a serious problem. If you don't know why, then go back to calc 101.

So your code should start like this:

syms x
f = log(x);
T = taylor(f, 'Order', 3,'expansionpoint',1)

Which works nicely.

T =
x - (x - 1)^2/2 - 1