Compute the absolute and relative errors in using c to approximate x.
x=e; c=2.74
approximate how? There are lots of methods.
c-e = 2.74-e = 0.00217
(c-e)/e = 0.00798 ≈ 0.8%
To compute the absolute and relative errors in using c to approximate x, we need to first determine the absolute error and then calculate the relative error.
Absolute Error:
The absolute error is the difference between the actual value (x) and the approximate value (c). In this case, x=e and c=2.74.
Absolute Error = |x - c|
Substituting the values:
Absolute Error = |e - 2.74|
Relative Error:
The relative error is the absolute error divided by the actual value (x) and is usually expressed as a percentage.
Relative Error = |x - c| / |x| * 100%
Substituting the values:
Relative Error = |e - 2.74| / |e| * 100%
To calculate the absolute and relative errors, we need to know the numerical value of e. The value of e is approximately 2.71828.