This preview shows page 1. Sign up to view the full content.
Unformatted text preview: −→ x ): R 3 → R which has Frstorder contact with f ( −→ x ) at −→ x = −→ x : v v v f ( −→ x ) − T −→ x f ( −→ x ) v v v = o ( b −→ x − −→ x b ) (3.3) which is to say lim −→ x → −→ x v v v f ( −→ x ) − T −→ x f ( −→ x ) v v v b −→ x − −→ x b = 0 . (3.4) When such an a±ne function exists, we call it the linearization of f ( −→ x ) or the linear approximation to f ( −→ x ) , at −→ x = −→ x . 5 Since functions with ±rstorder contact must agree at the point of contact, we know that T −→ x f ( −→ x ) = f ( −→ x ); then Remark 3.2.2 tells us that T −→ x f ( −→ x + △ −→ x ) = f ( x ) + ℓ ( △ −→ x ) . (3.5) 5 Properly speaking, it should be called the afne approximation ....
View
Full
Document
This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Derivative

Click to edit the document details