MAC2311 chapter 2 lecture outlines 091

MAC2311 chapter 2 lecture outlines 091 - MAC2311 Calculus I...

This preview shows pages 1–4. Sign up to view the full content.

1 MAC2311, Calculus I 2.1 The Tangent and Velocity Problems Secant line Tangent line Average rate of change The average rate of change in the function f(x) over the interval from x = a to x = a + h, can be found using the difference quotient which is really just the “slope” formula. average rate of change = ( ) ( ) f a h f a h + - The average rate of change in the function f(x) over the interval from x to a, can be found using the difference quotient, a verage rate of change = ( ) ( ) f x f a x a - - . Again, this is just the “slope” formula: 2 1 2 1 y y changein y or changein x x x - - . Instantaneous rate of change Average velocity Instantaneous velocity See exercises 2 and 6 on page 87 in the text.

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

View Full Document
2 MAC2311, Calculus I 2.2 The Limit of a Function Definition of a Limit: If f(x) becomes arbitrarily close to a unique number L as x approaches a from both sides, then we say the limit of f(x), as x approaches a, is L, and we write ( ) lim x a f x L = . Find limits graphically. The two most common types of problems where the limit does not exist… f(x) approaches a different value from the right of a than from the left. f(x) increases or decreases without bound as x approaches a. Note: The limit of f(x) as x approaches a does not depend on the value of f(x) at a. But sometimes we can use direct substitution and the limit will equal the value of f(x) at a. These are called “well- behaved” functions and are said to be “continuous” at a. One-sided Limits: ( ) lim x a f x L + = means “the limit of the function f(x) as x approaches a from the right is L.” ( ) lim x a f x L - = means “the limit of the function f(x) as x approaches a from the left is L.” Note: The ( ) lim x a f x L = if and only if ( ) lim x a f x L + = = ( ) lim x a f x L - = . Examples: Try exercises 2, 4, 8, 16, 26, 28 on page 96 in the text. Try exercise 6 with a partner.
3 MAC2311, Calculus I 2.3 Calculating Limits Using Limit Laws Properties of Limits (Limit Laws): Suppose that c is a constant and the limits ( ) lim x a f x and ( ) lim x a g x exist. Then…

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/12/2011 for the course MAC 2311 taught by Professor Teague during the Spring '11 term at Santa Fe College.

Page1 / 7

MAC2311 chapter 2 lecture outlines 091 - MAC2311 Calculus I...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online