We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byLilly Hershey
Modified over 2 years ago
Take It To the Limit Limits of Functions
A limit example Suppose the frog can only hop half-way to the stream on each hop. Would he ever get to the water?
Reaching the Limit If half the remaining distance is covered with each jump, theoretically the frog will never reach the stream. The stream represents the limit. Limits in mathematics are similar.
Definition of a limit (informal definition)If f(x) becomes arbitrarily close to a single number L as x approaches c from either side, the limit of f(x), as x approaches c, is L.
An Example Suppose you are asked to find the limit of the function:
Solution to the ExampleReplace the variable (x) with the number –1. This would result in the following:
Example Using Excel SpreadsheetGiven the limit problem: Notice what happens when you evaluate numbers closer and closer to 2
A graphical illustrationGiven the limit to evaluate Graph the function: f(x) = 2x-5
Table view of function Notice at the value x=2, the f(x) or y value is -1
Conclusion Limits of functions can be found by evaluating the function for the value the variable is approaching, provided the function is defined at that value.
Copyright © Cengage Learning. All rights reserved.
Limits and Derivatives 2. The Limit of a Function 2.2.
Limits and Their Properties 1 Copyright © Cengage Learning. All rights reserved.
Introduction to Limits. What is a limit? A Geometric Example Look at a polygon inscribed in a circle As the number of sides of the polygon increases,
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.
Notes Over 1.6 Solving an Inequality with a Variable on One Side Solve the inequality. Then graph your solution. l l l
Introduction to Limits Section 1.2. What is a limit?
Copyright © Cengage Learning. All rights reserved. 2 Limits and Derivatives.
Copyright © Cengage Learning. All rights reserved. 10 Introduction to the Derivative.
Copyright © Cengage Learning. All rights reserved. 3 Introduction to the Derivative.
Table of Contents Rational Functions: Vertical Asymptotes Vertical Asymptotes: A vertical asymptote of a rational function is a vertical line (equation:
Solving Systems of Equations by Substitution by Tammy Wallace Varina High School.
Limits and Their Properties Copyright © Cengage Learning. All rights reserved.
Solve Absolute Value Inequalities © 2011 The Enlightened Elephant.
Section 1.2 – Finding Limits Graphically and Numerically
Copyright © Cengage Learning. All rights reserved. 3 Applications of Differentiation.
Projectile Motion Motion in two dimensions © 2006 Certiport.com.
Limits Involving Infinity Infinite Limits We have concluded that.
A radical equation is an equation that contains a radical.
Linear Inequalities in one variable Inequality with one variable to the first power. for example: 2x-3<8 A solution is a value of the variable that makes.
5.5 Direct Variation Pg Math Pacing Slope Review.
Limits and Derivatives
Linear Equation: an equation whose graph forms a line. is linear. is not. In linear equations, all variables are taken to the first power. Linear means.
Climatic Graph Tutorial Start We can use this Excel spreadsheet to plot the climatic graph with the data in this table. End.
Look at website on slide 5 for review on deriving area of a circle formula Mean girls clip: the limit does not exist https://www.youtube.com/watch?v=oDAK.
1.2 Finding Limits Graphically & Numerically. After this lesson, you should be able to: Estimate a limit using a numerical or graphical approach Learn.
THE SCIENTIFIC METHOD. THE SCIENTIFIC METHOD: is a process used to find answers to questions about the world around us is an organized series of steps.
Inequalities and their Graphs Objective: To write and graph simple inequalities with one variable.
Copyright © Cengage Learning. All rights reserved. The Limit of a Function 1.3.
HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems College Algebra.
LIMITS OF FUNCTIONS. CONTINUITY Definition (p. 110) If one or more of the above conditions fails to hold at C the function is said to be discontinuous.
Table of Contents Rational Functions: Slant Asymptotes Slant Asymptotes: A Slant asymptote of a rational function is a slant line (equation: y = mx + b)
Interpretation of Domain and Range of a function f.
What is the difference between > and What is the difference between > and ? What do these differences mean when graphing? Topic #11: Linear Inequalities.
3.1 Solving Systems Using Tables and Graphs When you have two or more related unknowns, you may be able to represent their relationship with a system of.
6.5 Graphing Linear Inequalities
4.4 Equations as Relations
Section 11.1 Limits.
Lesson 15-1 Limits Objective: To calculate limits of polynomials and rational functions algebraically To evaluate limits of functions using a calculator.
The Scientific Method By: Wanda S. Roberts The Scientific Method: Teacher: Wanda Roberts Grade level: 7th Subject area: Science Standards: S7CS5 Use.
Graphing Systems of Equations Graph of a System Intersecting lines- intersect at one point One solution Same Line- always are on top of each other,
Hawkes Learning Systems College Algebra
Mr. Cesaire Martin Van Buren High School
Inverse Functions Lesson Back to the Magic Box What if we cram a number up the spout and out of the funnel pops the number that would have given.
Limits Section WHAT YOU WILL LEARN: 1.How to calculate limits of polynomial and rational functions algebraically. 2.How to evaluate limits of functions.
Solving Absolute Value Inequalities
© 2017 SlidePlayer.com Inc. All rights reserved.