lecture12 - Math 006 (Lecture 12) Introduction to Limits...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 006 (Lecture 12) Introduction to Limits Example 1. Graph the function f ( x ) = x 2 - 1 x + 1 . Definition 1. We write lim x c f ( x ) = L or f ( x ) L as x c if the function value f ( x ) is close to the single real number L whenever x is close to, but not equal to c . Example 2. Let h ( x ) = | x | x . Find h (0) and lim x 0 h ( x ). We saw that the values of the function h ( x ) approached two different numbers, depending on the direction of approach, and it was natural to refer to these value as “the limit from the left” and “the limit from the right”. Definition 2. We write lim x c - f ( x ) = K, ( lim x c + f ( x ) = H ) and call K the left-hand limit of f ( x ) ( H the right-hand limit of f ( x )) whenever x is close to c , but to the left (right) of c . 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Example 3. Find lim x 0 + h ( x ) and lim x 0 - h ( x ). Theorem 1. A limit exists if and only if the corresponding left-hand limit and the right- hand limit are equal . That is, lim x c
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

Page1 / 3

lecture12 - Math 006 (Lecture 12) Introduction to Limits...

This preview shows document pages 1 - 3. Sign up to view the full document.

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