Question

I need help with a MATLAB problem.
Write a MATLAB function to compute the exponential function directly from the Taylor series: e^x=1+x+X^2/2!+x^3/3!.... The series should end when the last term is less than 10^-6. Test your function against the built in function exp, but be careful not to make x too large-this could cause rounding error.

Can anyone help me??

Answer 1

If we notice that the terms of the Taylor's series are such that the nth term is the previous term multiplied by x/n, considering the initial "1" as the zeroth term.

This means that instead of calculating each term from scratch, we only need to multiply the previous term by x/n to get the present term.

1 (term zero)
x (term zero * x /1 )
x^2/2! = x* (x/2)
x^3/3! = x^2/2! * (x/3)
...
the running sum calculated will be the various approximation for exp(x).
A check should be incorporated to stop calculations when the term is less than 10^(-6)

Answer 2

I kind of understand what you are saying but I'm confused on how to write the actual code.

Answer 3

Hint:
Pseudocode:
Function Exp(x)
initialize term, sum, n
while (term>10^(-6))
term=term*(x/n)
sum=sum+term
n=n+1
end while
return sum

Give it a try with Matlab and post your code if you need help.

Answer 4

OK thanks I will post my code if I need more help

Answer 5

You're welcome! :)

Answer 6

I am still having issues with this code. Can someone help me correct it so that I can run right.
Thanks

Answer 7

This is where defining variables (in English) is important when programming so that we do not confuse the values.

In your code, y is used to return the value of the function, which is the sum of the series. That's ok.

In the lines
while y>10^-6
y=y*(x/n);
y represents the value of each term of the series, which is not the sum of the series.
Also, y must assume a value before we can do the recursive statement
y=y*(x/n)
This initial value must be defined before entering the while loop.
Similarly, n and sum must be initialized to appropriate values before entering the loop.
(n=1, sum=0),
Finally, y=sum (because y is the return value equal to sum) must be placed at the end.

Try to make corrections and post if you can.