After completing this section, students should be able to do the following.Recognize when a limit is indicating there is a vertical asymptote.Evaluate the limit as xx approaches a point where there is a vertical asymptote.Match graphs of functions with their equations based on vertical asymptotes.Discuss what it means for a limit to equal ∞∞.Define a vertical asymptote.Find horizontal asymptotes using limits.Produce a function with given asymptotic behavior.Recognize that a curve can cross a horizontal asymptote.Understand the relationship between limits and vertical asymptotes.Calculate the limit as xx approaches ±∞±∞ of common functions algebraically.Find the limit as xx approaches ±∞±∞ from a graph.Define a horizontal asymptote.Compute limits at infinity of famous functions.Find vertical asymptotes of famous functions.Identify horizontal asymptotes by looking at a graph.Identify vertical asymptotes by looking at a graph.
Ohio Transfer Module Mathematics, Statistics, and Logic (TMM) Standards
Core TMM005 Outcome: Core skill demonstrated by students who successfully complete a Calculus I Course
Standard: Determine the derivative of a function using the limit definition and derivative theorems. Interpret the derivative as the slope of a tangent line to a graph, the slope of a graph at a point, and the rate of change of a dependent variable with respect to an independent variable.