My graph for a while loop approximation is blank!

I have tried to find the solution to this but can't seem to figure it out. I know that my values are scalar and that's why they are coming out blank, but I don't know how to vector them in order to graph them. This is the code I am trying to graph. I also need to have the graph compare my e^x approximation with the actual e^x value. This code is being run at x=3

      figure
      grid on
      hold on
      xsize = 0:2;
      n = 0;
      ex = 0;
      while n < 3    
          ex = ex + x.^n/factorial(n);
          n = n + 1;
          plot(xsize,ex,xsize,exp(x))
      end

EDIT: This graph is meant to be shown as a function of n, which is why 'xsize' = 0:2 because I am only graphing a 3 term approximation

[madhan ravi]

Is x a symbolic variable?

Answer 1

[Tejas Jayashankar]

Hi Thomas,

You should not be plotting the graph within every iteration of the loop. As you mentioned, you need a vector of values to plot the approximation to e^3. So if you make ex a vector and accumulate the various terms of the Taylor series expansion in each iteration, you can plot out your results at the end as follows:

x = 3;
figure;

hold on
xsize = 0:500;
n = 0;
ex = 0;

while n < xsize(end)    
  ex = [ex; x.^n/factorial(n)];
  n = n + 1;
end

plot(xsize, cumsum(ex), [0 xsize(end)], [exp(3) exp(3)])
ylim([0 30])

In the while loop I am accumulating each term of the taylor series expansion into a vector. So the vector would be

[0  1  x  x^2/2!  x^3/3! ...]

for some general value x, which is 3 in your case. Outside the while loop, when you want to plot the approximation for each value of n, just perform a cumulative sum using the cumsum function. To plot the actual of e^3 you need to specify the starting and ending coordinates of the line in the plot function.

[Stephen23]

+1 nice clear explanation. Better would be to not use any loop.