Daily Prep 1B -- MTH 201-04

--- tags: mth201, dailyprep --- # Daily Prep 1B -- MTH 201-04 ## Overview Finding an object's instantaneous velocity, or the instantaneous rate of change in a function, involves setting up a sequence of average rates of change over smaller and smaller intervals, and as the intervals get smaller we look to see what the average rates of change on those intervals approaches. This concept of "letting a value approach something and see what the results approach" comes up over and over again in calculus, so we invent a new tool for it: the **limit**. In Module 1B, we'll introduce the concept of the limit and learn how to find limits using tables, graphs, and formulas. We'll also look at variations on the idea of a limit where we look at only one direction of approach, and where the "approach" is to let the input go to infinity. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. + Explain the notation used for limits. + Find the limit of a function as the input approaches a point, using tables and graphs. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. + Find the limit of a function as the input approaches a point, using algebraic simplification. + Find the instantanous velocity of a moving object by setting up and computing a limit. ## Resources for learning **Reading:** Read through [Section 1.2](https://activecalculus.org/single/sec-1-2-lim.html) of the _Active Calculus_ text. **Video:** Watch the following videos and take notes. The total running time is 28:47. + Screencast 1.2.1: Limits (6:02) https://www.youtube.com/watch?v=GZzJOAUOqLI + Screencast 1.2.2: Limits of functions using graphing tools (6:27) https://www.youtube.com/watch?v=5TFu_sh_orM + Screencast 1.2.3: Limits of functions using tables (5:58) https://www.youtube.com/watch?v=GdBIiRzaTAQ + One-Sided Limits, example 1 (6:55) https://www.youtube.com/watch?v=JXVUyk2JOU4 + How to find limits at infinity using a graph (3:25) <-- This also includes a nice example of one-sided limits https://www.youtube.com/watch?v=5IKlWJUmRVo ## Exercises The exercises for this Daily Prep are packaged as a **Desmos activity**. To access it, go to student.desmos.com and log in with your Desmos account. If you have successfully joined the Desmos class roster as part of the *Tools Assignment*, you will see "Daily Prep 1A" available in a list. Click the link to begin, and continue through the end. Your work is saved as you enter it, so there is nothing to "submit" at the end. ## Submission and grading  A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.