"Calculus and its applications: " - 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 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 LIMIT PROPERTIES: If and then we have the following: The limit of a constant is the constant. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide LIMIT PROPERTIES (continued): 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. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide LIMIT PROPERTIES (continued): The limit of a sum or difference is the sum or difference of the limits. The limit of a product is the product of the limits. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide LIMIT PROPERTIES (concluded): The limit of a quotient is the quotient of the limits. The limit of a constant times a function is the constant times the limit. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide Example 1: Use the limit properties to find We know that By Limit Property L4, Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide Example 1 (concluded): By Limit Property L6, By Limit Property L1, Thus, using Limit Property L3, we have Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide THEOREM ON LIMITS OF RATIONAL FUNCTIONS For any rational function F, with a in the domain of F, Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide 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 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 LIMIT PROPERTIES: If and then we have the following: The limit of a constant is the constant. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide LIMIT PROPERTIES (continued): 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. Algebraic Limits and Continuity 2012 Pearson Education, Inc. All rights reserved Slide LIMIT PROPERTIES (continued): The limit of a sum or difference is the sum or difference of the limits. The limit of a product is the product of the limits. Algebraic Limits and Continuity 2012 .
