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3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 To Infinity and Beyond By the end of this lesson, Buzz Light Year will be able to: 1.) Determine whether a function approaches infinity. 2.) Find vertical/horizontal asymptotes of functions. 3.) Understand the properties of infinite limits. 4.) Evaluate the limit of a function as x approaches infinity. 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Solutions to Evaluating Limits 1.) 2.) March 05, 2014 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Infinite Limit A function in which y increases or decreases without bound as x approaches c is said to have an infinite limit. Take a look at WS6--Limits: A Graphical Approach! 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Ex. 1) Evaluate the limit as x approaches two of x 1.5 1.9 1.99 1.999 2.001 2.01 2.1 2.5 f(x) 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Ex. 2) Use a graphing calculator to determine the limit of the following functions. 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Infinite limit = Vertical asymptote If y approaches as x approaches c from the right or left, then the line x=c is a vertical asymptote. 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Ex. 3) Determine all vertical asymptotes of the graph March 05, 2014 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Properties of Infinite Limits Let c and L be real numbers and f and g be functions such that 1.) Sum or difference 2.) Product 3.) Quotient 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Ex. 4) Evaluate the limits, using properties where applicable. a.) b.) c.) 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Limits at Infinity vs. Infinite Limits March 05, 2014 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Limits at Infinity Ex. 5) Use the table below to evaluate the limit. x f(x) -100 -10 -2.997 -2.97 -1 0 1.5 0 1 10 100 1.5 2.97 2.9997 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Ex. 6) Find the limit. March 05, 2014 3-3,3-5 Infinite Limits and Limits at Infinity.notebook March 05, 2014 Limits at infinity = Horizontal asymptote 3-3,3-5 Infinite Limits and Limits at Infinity.notebook # # # March 05, 2014 # 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Ex. 7 Find the limit. March 05, 2014 3-3,3-5 Infinite Limits and Limits at Infinity.notebook Homework Page 84 Exercises 1-4,25-44 Page 193 Exercises 1-6, 11-20 March 05, 2014