Linear approximation (or linearization) is a method of estimating a value on a function by placing that value on a tangent line of the function at a nearby value. This approximation can be found with the formula:
with being the nearby value, being the exact value, and being the approximation. Since a tangent line is being used, accuracy decreases the further apart and are. A linear approximation is a Taylor approximation of the first degree.
To find , the steps would be as follows:
(This is the operation being applied)
(The derivative of the function)
(All values substituted into the formula, is given the nearby value of )
This value is quite close to the actual square root of which is approximately .