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Calculus and its applications: 1.2

"Calculus and its applications: 1.2" - Algebraic limits and continuity have objective: develop and use the limit principles to calculate limits, determine whether a function iscontinuous at a point. | 2012 Pearson Education, Inc. All rights reserved Slide 1.2- Algebraic Limits and Continuity OBJECTIVE Develop and use the Limit Principles to calculate limits. Determine whether a function is continuous at a point. 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES: If and then we have the following: L.1 The limit of a constant is the constant. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES (continued): L.2 The limit of a power is the power of the limit, and the limit of a root is the root of the limit. That is, for any positive integer n, and assuming that L ≥ 0 when n is even. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES (continued): L.3 The limit of a sum or difference is the sum or difference of the limits. L.4 The limit of a product is the product of the limits. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES (concluded): L.5 The limit of a quotient is the quotient of the limits. L.6 The limit of a constant times a function is the constant times the limit. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- Example 1: Use the limit properties to find We know that By Limit Property L4, 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- Example 1 (concluded): By Limit Property L6, By Limit Property L1, Thus, using Limit Property L3, we have 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- THEOREM ON LIMITS OF RATIONAL FUNCTIONS For any rational function F, with a in the domain of F, 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- Example 2: Find The Theorem on Limits of Rational Functions and Limit Property L2 tell us that we | 2012 Pearson Education, Inc. All rights reserved Slide 1.2- Algebraic Limits and Continuity OBJECTIVE Develop and use the Limit Principles to calculate limits. Determine whether a function is continuous at a point. 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES: If and then we have the following: L.1 The limit of a constant is the constant. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES (continued): L.2 The limit of a power is the power of the limit, and the limit of a root is the root of the limit. That is, for any positive integer n, and assuming that L ≥ 0 when n is even. 1.2 Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 1.2- LIMIT PROPERTIES (continued): L.3 The limit of a sum or difference is the sum or difference of the limits. L.4 The limit of a product is the product of the limits. 1.2 Algebraic Limits and Continuity 2012 .