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• Distinguish between limit values and function values at a point. • Understand the use of neighborhoods and punctured neighborhoods in the evaluation of one-sided and two-sided limits. • Evaluate some limits involving piecewise-defined functions. PART A: THE LIMIT OF A FUNCTION AT A POINT
2.2.1 Using correct notation, describe the limit of a function. 2.2.2 Use a table of values to estimate the limit of a function or to identify when the limit does not exist. 2.2.3 Use a graph to estimate the limit of a function or to identify when the limit does not exist. 2.2.4 Define one-sided limits and provide examples.
Unit 1 - Limits and Continuity. 1.1 Can Change Occur at an Instant? 1.2 Defining Limits and Using Limit Notation. 1.3 Estimating Limit Values from Graphs. 1.4 Estimating Limit Values from Tables. 1.5 Determining Limits Using Algebraic Properties. (1.5 includes piecewise functions involving limits)
Unit 1 Practice Test: Limits. Date: Here’s your chance to show what you know! You’ve got all you need in your brain, so trust yourself and put your calculator away. Make sure you show me all the cool work you can do to get your answer when appropriate. 1. Find the following limits if.
This theorem allows us to calculate limits by “squeezing” a function, with a limit at a point a that is unknown, between two functions having a common known limit at a. Figure 2.27 illustrates this idea.
Definition of a Limit. Read this section to learn how a limit is defined. Work through practice problems 1-6. Practice Problem Answers. Practice 1: (a) 3 − 1 <4x − 5 <3 + 1 3 − 1 <4 x − 5 <3 + 1 so 7 <4x <9 7 <4 x <9 and 1.75 <x <2.25: 1.75 <x <2.25: " x x within 1/4 1 / 4 unit of 2 2 ".
Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point.
