STAT312 Lecture : Taylor’s Theorem.pdf

• School: University of Alberta
• Department: Statistics
• Course: STAT312
• Professor: Douglas Wiens

Document Summary

Taylor s theorem: su ciently smooth functions can be approximated locally by polynomials. sup- If cated, function of say that the series lim. Represents the function is a, generally quite compli- we. It is indeed true in this example that. We will later show that it does so in a nice uniform way; for now it is enough to show that it does so for any particular point. | | and keep it xed. ( + 1) ( + 2) ( + Example: pand around 0: ( ) = log (1 + ) with | (0) = 0 and for. 0: ( )( ) = ( 1) +1 ( Then for some with | | log (1 + ) Write this as log (1 + ) = ( ) + ( ); we will later derive a more re ned expression for ( ) ( integral form of the remainder ) from.