The function f(x) = e^x can be represented in a Taylor series by e^x = sigma^inf

Question

The function f(x) = e^x can be represented in a Taylor series by e^x = sigma^infinity x^n. Write a n = 0_n! MATLA8 function named Taylor_series that determines e^x by using the Taylor series representation. The function should use a while loop to calculate e^x by adding terms of the series and stop when the absolute value of the term that was added last is smaller than 0.0001. The function should accept one input (a value for x) and return two outputs (the number of terms added in the series and the total sum accumulated) (Use MATLAB function factorial for computing nl). Call your function with an Input value of x = 10.

Explanation / Answer

Hey heres the code:

fact.m:
function f = fact(n)
f = prod(1:n);

main.m:
power = @(x, n) x.^n;

s = power(2, 3)

x=10

ts=0

i=0
while 1
   if ts < 0.0001
     
      break
  
   end
   ts=ts+power(x,i)/fact(i)
   i=i+1
end
disp(ts)

where ts is the final result of series.

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