Matlab Programming(Need help with the last couple of details)

[ialan731]

Homework Statement

Okay, so I need some help with this Matlab program. I never learned Matlab, so I'm trying to do it as best as I can. The question is: Calculate the 2nd and 3rd degree Taylor polynomials for the function f(x)=ln(1+x) about the point a=0 Plot these polynomials and the function on the interval -1<x<3

Homework Equations

N/A

The Attempt at a Solution

This is what I have so far. I thought it was right, but Matlab said "Not enough input arguments." What does that mean, and I how do I fix it?
>> figure(1);clf;
x=[-1:.01:3];
y=log*(1+x);
P2= x-(x^2/2)!;
P3= x-(x^2/2)+(x^3/3)!;
figure(1);clf;
plot(x,y,x,P2,'--',x,P3,'-.')
legend('log*(1+x)','P_2','P_3')
xlabel('x')
title('The function and the 2^{nd} and ^{rd} order Taylor Polynomials')
figure(2);clf
plot(x,abs(y-P2),x,abs(y-P3),'--')
legend('log*(1+x)-P_2|','log*(1+x)-P_3|')
xlabel('x')
title('Errors in the two Taylor Polynomials')

Thanks in advance!:)

 

[lewando]

Problem is with this line: "y=log*(1+x)". Can you spot it?

 

[ialan731]

Honestly, no. There was an issue with that line before because I had put ln instead of log so I changed it. Is there supposed to be a . Before/after the x? I noticed that there's a lot of times where that's necessary.

 

[lewando]

log (natural log) is a function so it should be: "y=log(1+x)"

 

[ialan731]

It's that simple? Wow I was looking for at least an hour, and I couldn't find the issue. Thank you so much!

 

[lewando]

I think you are also going to have a problem with the factorial operator. Missed that one--try the factorial() function. [edit-- you have some significant semantic issues with the factorial operation--does not make much sense]

 

[ialan731]

What do you mean?

 

[lewando]

Well for example, the line:
P2= x-(x^2/2)!;

You are trying to take the factorial of an array of non-integers (not defined) using "!" (not a MATLAB operator). You might need to step back and detail what you are trying to do.

 

[ialan731]

Oh so I would have to write out the factorial instead of simply putting !.

 

[lewando]

I don't understand what the factorial symbol is doing in the expressions for P2 and P3. I don't think they belong there at all.

 

[ialan731]

But doesn't the equation call for a factorial? How else would it be done?

 

[lewando]

Not sure what equation you are using. From page 4 of this link is the general form http://www.math.ufl.edu/~vatter/teaching/m8w10/m8l01.pdf

f = ln(1+x)
f' = 1/(1+x)
f'' = -1/(1+x)²
f''' = 2/(1+x)³

[edit-- also familiarize yourself with the distinction between the ".^" and the "^" operators]

 

[ialan731]

Not sure what equation you are using. From page 4 of this link is the general form http://www.math.ufl.edu/~vatter/teaching/m8w10/m8l01.pdf

f = ln(1+x)
f' = 1/(1+x)
f'' = -1/(1+x)²
f''' = 2/(1+x)³

[edit-- also familiarize yourself with the distinction between the ".^" and the "^" operators]

I have to use the Taylor series so it's not just the derivative. And okay, will do.