# Linear Approximations Accuracy

## Applications of Linear Approximation and Accuracy

Note, x - a is often symbolized by Δx

Dealing with Linear Approximation, we are dealing with calculations that are… approximate. In this there is a margin for error, and some results are more accurate than others.

#### Definition - Linear Approximation Error

If the variable x-value is measured as x = a, with the error as Δx (or x - a) units, then the Δf can be the error in estimating our f(x),

Δf = f(x) - f(a) =roughly= f’(a)Δx

### Linear Approximation Cube  ### Linear Approximation Error    ### Linear Approximation Error  ## Relative Error and Percentage Error

What we have been working with above is the absolute error. This gives, as the name suggests, the pure value of the error. However, it is not an error value comparable between different types of measurements. For example, an error when measuring the distance between two cities of 1 meter, is not the same as a an error of measuring shoe size of 1 meter. This is where we introduce Relative Error and Percentage error, to give us a better understanding of the relevance of error.

### Definition - Relative Error

Relative Error =
error in f
value of f
=
Δ f
f

### Definition - Percentage Error

Percentage Error is simply Relative Error as a Percentage

Δ f
f
x 100

### Relative Error  