l_notes09 - Lecture IX Linear Approximation 1 Onevariable...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture IX Linear Approximation 1 One-variable Functions Let f be a one-variable function on a domain D . If f is differentiable at x = c , we say f has a linear approximation, which we deFne in the following way. Defnition 1 If f is a function differentiable at c , for any x deFne Δ f = f ( x ) f ( c ) and Δ x = x c . There exist a scalar A c and a function c ( x ) such that Δ f = A c Δ x + c ( x x and lim c ( x ) = 0 . x c Then Δ f A c = f ( c ) and c ( x ) = Δ x f ( c ) . We say that f has a linear approximation at c and that the expression Δ f app = f ( c x is a linear approximation formula for f at c . The function c is called the relative error function for f at c . 2 Multivariable Functions Defnition 2 Let f be a multilinear function and let P be a point in its domain D in E 2 . DeFne Δ f = f ( a + Δ x, b + Δ y ) f ( a, b ) . We say that f has linear approximation at P if there exist scalars A , B and functions 1 , 2 such that: 1. for all
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/24/2011 for the course MATH 1802 taught by Professor Duorg during the Two '04 term at Macquarie.

Page1 / 2

l_notes09 - Lecture IX Linear Approximation 1 Onevariable...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online