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| '''Linearization''' is a simple method for estimating an unknown value given by a function. | '''Linearization''' is an approximation method. |
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| To estimate an unknown value ''f(x)'', pick a value ''a'' near ''x'' with a known value for ''f(a)''. Using the slope (derivative) at ''a'' and the value of ''f(a)'', estimate ''f(x)'' as: | A function ''f'' is given such that ''f(a)'' and ''f'(a)'' (i.e., the [[Calculus/Derivative|first derivative]]) are known, but ''f(x)'' for some ''x'' near ''a'' is not known. The linearization of ''f'' is used to approximate ''f(x)'' as: |
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| {{attachment:linearization}} | {{attachment:uni.svg}} This approximation method works in the multivariate case as well. [[Calculus/PartialDerivative|Partial derivatives]] are usually notated like ''f,,x,,'' here. For example, for ''x'' near ''a'' and ''y'' near ''b''... {{attachment:bi.svg}} |
Linearization
Linearization is an approximation method.
Contents
Usage
A function f is given such that f(a) and f'(a) (i.e., the first derivative) are known, but f(x) for some x near a is not known. The linearization of f is used to approximate f(x) as:
This approximation method works in the multivariate case as well. Partial derivatives are usually notated like fx here. For example, for x near a and y near b...
