Need help with an if loop

I need help generating an 'if' loop to calculate the approximate f(x)=exp(5) in matlab

I don't understand how to do these loops and would appreciate some assitance in learning them

Thank you in advance

Answer 1

[Shubham Gupta]

First, exp(x) has an expansion as follows:

Now, how to define infinity?

When , . So, we check if this term is close to zero? Depending on that we can say that our estimation has converged. Now, to code this

function y = exp_mm(x)

y = 1; % initial estimation
n = 1; % initial n

while 1
    add_term = (x^n)/factorial(n);  % additional term x^n/(n!)
    if abs(add_term)<1e-6           % check if it's close to zero?
        break;                      % break if it's close to zero
    else
        y = y + add_term;           % else we continue adding the term
        n = n+1;                    % and increase the n
    end
end

Here are some comarison:

y = exp(5)

% Outputs:
y =

  148.4132
  
y1 =exp_mm(5) 

% Outputs:
y1 =

  148.4132

Pretty close to what we wanted. We can calculate error now,

error = y-y1

% Output:
error =

   1.1981e-07

So, our value is correct at least of the 1e-6.

I hope this help! Let me know if you have doubts.