Help with while loop

Hello,

I have to create a program that will find the taylor series expansion at an arbitrary value x. I also have to find the relevant error of the series expansion from the true exp.

Create a MATLAB program to compute this series and stop at %error < 3%. Display the value of the series approximation and how many terms that you used to calculate this value.

x=1.5;
y=0;
n=0;
error=0;

while(error>3)
  if n<2
    f=1;
  elseif n>=2
    f=f*n;
  end
  y=y+(x^n/(f));
  error=((exp(x)-y)/exp(x))*100;
  n=n+1;
end
disp(n-1)
disp(error)

This is currently what I have but my program will only compute for the first n. I can not seem to see what is going wrong and would appreciate any hints.

Answer 1

[Matt Fig]

You were pretty close, but there are a couple of mistakes.

1. You start out the error at zero, then ask the loop to run only when the error is greater than 3....
2. You are not actually calculating the factorial for each new value of n.
3. You need to use the absolute value when calculating the error.

x=1.5;
y=0;
n=0;
ER=100;  % Don't name a variable 'error'.  Start >3 so loop runs!

while(ER>3)

    f = 1;
    for ii=2:n
      f=f*ii;
    end

    y = y+(x^n/(f));
    ER = (abs(exp(x)-y)/exp(x))*100;
    n=n+1;
  end
  disp(n-1)
  disp(ER)

[Stephen]

Thanks Matt! It seems so obvious now that I should have started ER 100% instead of 0%. I have also changed the variable error to ER and made some changes to the factorial and it all works now!

Answer 2

[Jan]

You start at "n=0" and use "f=1" for the first two terms. In addition you want to measure the positive(!) distance between the approximation and the true result. Therefore you need the ABS() function.

Btw, do not overwrite the important function error by a local variable. Although this does not cause an error here, it will in any larger program with error handling.

[Stephen]

Thanks for the reply Jan! We are not aloud to use built in functions for this specific problem. I said n=0 since the summation starts from zero and I used the if/elseif statements for f to deal with the factorial since we couldn't use that function either(0!=1). For the first part to calculate the series with 15 n terms I used this script file:

x=1.5;

y=0;

for n=[0:4];

if n<2

f=1;

elseif n>=2

f=f*n;

 end
     y=y+(x^n/(f));

end y

exponential=exp(x)

I received the correct answer using this but now I don't know how many n terms I need that will satisfy the error condition. Tee code in my first post is my attempt and when I go through it by hand it makes sense to me but matlab stops with the first term.

[Jan]

Your program does contain over a dozen of built-in function calls. Teachers ask sometimes very stupid questions... See Answers: what can be programmed without built-ins