We do this throughout the course via our text homework using an online homework system. How do we make a prediction Zoom into the neighboring points. Here’s how I learned to enjoy them: What is a limit Our best prediction of a point we didn’t observe. We expect that they can easily move from a limit statement to a graphical or numerical representation that behaves in the same way.Īdditional Notes : There are no synthesis questions for this activity but it is important to assign homework questions over this material. Limits, the Foundations Of Calculus, seem so artificial and weasely: Let x approach 0, but not get there, yet we’ll act like it’s there Ugh. ![]() ![]() They should understand the limit definitions of vertical and horizontal asymptotes as well as be able to recognize asymptotes graphically. Need to Establish by the End of Activity/Wrap-Up : Students should leave this activity understanding limits graphically, numerically and algebraically (not using an epsilon delta definition though). In the case of rational functions they are a more interesting characterization than a characterization using rate of change. Limits are another way to characterize the behaviour of functions. Introduction/Motivation of the Activity : This activity can be motivated through the characterization of functions. It also uses their understanding of what exponential functions and power functions are. Ideas this Activity Builds On : This activity builds on students intuitive ideas of getting "closer and closer" to something and "getting larger and larger" as well as their graphical understanding of asymptotes. Q7 is difficult for the students and is best done in class. Q6 is an important whole class discussion where the limit definition of asymptotes is established using students graphical understanding of asymptotes and the understanding of limits they have developed in this activity. For problems 3 7 using only Properties 1 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points. Again for Q5 it is best if students work individually, then in small groups and then as a whole class. For Q4, students should work individually, then in small groups and then be ready to participate in whole class discussion. It is important to establish in 3d that any exponential function will eventually dominate over any power function and consider the implications of this for the limits on the previous page. This activity generally takes two days in class to complete and somewhere in Q3 is a good breaking point as after an initial discussion of this problem students can complete this problem at home and return ready to discuss their findings. There may be points in this work that you would like to call the class together to share the progress that they have made. Purpose : To develop students understanding of limiting behavior numerically, graphically and algebraically.Ĭlassroom Procedure : After an initial introduction to this activity students will work on the first two problems in small groups.
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