Compute the absolute and relative errors in using c to approximate x.
x=e;c=2.68
e=2.718
so, the
abs error is 2.718-2.68 = 0.038
as a % error, that is .038/e = 1.39%
To compute the absolute and relative errors in using c to approximate x, we need to first determine the actual value of x and then compare it to the approximate value using c.
Given that x = e ≈ 2.71828 (approximately), and c = 2.68, we can proceed with calculating the absolute and relative errors.
1. Absolute Error:
The absolute error is the absolute difference between the approximate value and the actual value. It provides a measure of how far off the approximation is from the real value.
Absolute Error = | x - c |
= | 2.71828 - 2.68 |
= 0.03828
Therefore, the absolute error in using c to approximate x is approximately 0.03828.
2. Relative Error:
The relative error is the absolute error divided by the actual value. It gives a measure of the error relative to the magnitude of the actual value.
Relative Error = Absolute Error / | x |
= 0.03828 / 2.71828
≈ 0.0141
Therefore, the relative error in using c to approximate x is approximately 0.0141, or 1.41% (rounded to two decimal places).
Note: Keep in mind that these calculations assume you are using the given values of x = e and c = 2.68. If you have different values, you can substitute them into the calculations to find the corresponding absolute and relative errors.
To compute the absolute and relative errors in using c to approximate x, we first need to calculate the absolute error.
Absolute Error:
The absolute error is the difference between the actual value (x) and the approximate value (c).
Absolute Error = |x - c|
In this case:
Absolute Error = |e - 2.68|
Next, we can calculate the relative error.
Relative Error:
The relative error represents the ratio of the absolute error to the actual value (x).
Relative Error = (|x - c|) / |x|
In this case:
Relative Error = (|e - 2.68|) / |e|
Please note that the value of e is approximately 2.71828 (a mathematical constant representing Euler's number) and may be different from the actual value you are referring to.