In otherwords,for valuescloseto the tangentline to the graphof a function at the point
providesan approximationof or We call this thelinearortangent
line approximationof at and indicateit by the formula
The linearapproximationcan be usedto approximatefunctionalvaluesthat deviateslightlyfromknown
values.The followingexampleillustratesthis process.
Example1:
Use the linearapproximationof the function at to approximate.
Solution:
We knowthat. So we will find the linearapproximationof the functionand substitute
valuescloseto
We note that
We also knowthat
By substitution,we have