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The inverse of the mathematical constant e can be approximated as follows:
Write a script that will loop through values of n until the difference between the approximation and the actual value is less than 0.0001. The script should then print out the built-in value of e -1 and the approximation to 4 decimal places, and also print the value of n required for such accuracy.
Matlab
Ch5Ex20.m
% Approximates 1/e as (1-1/n)^n, and determines
% the value of n required for accuracy to 4 dec. places
actual = 1 / exp(1);
diff = 1;
n = 0;
while diff >= 0.0001
n = n + 1;
approx = (1 - 1/n)^n;
diff = actual - approx;
end
fprintf('The built-in value of 1/e is %.4f\n',actual)
fprintf('The approximation is %.4f\n',approx)
fprintf('The value of n is %d\n',n)
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