MAC2311 chapter 2 lecture outlines 091

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

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

View Full Document Right Arrow Icon
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.
Background image of page 1

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

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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…
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

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

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

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