Section: Week 03: Sept. 6 | MAT 112A (Fall 2021) - Calculus I and Modeling | Davidson College

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Week 03: Sept. 6

  • Week 03: Sept. 6

    • Read 3.1; Formality of the page 134 rules will not be emphasized, but the conceptual introduction in previous pages is helpful, and you still need to understand all examples.
      3.1; 9, 10, 11, 12, 21, 22.  (On 21 & 22 and throughout Calculus, you must use Radians.)
      On all that follow, use good notation to show steps or explain reasoning; just an answer will not suffice.
      3.1; 38, 41, 45, 61, 79, 95, 96(Do you need to know constants are positive?).

    • Read 3.2.
      3.1; 50, 54, 55 on all three, show algebra steps as in class and/or explain reasoning in a sentence; just an answer will not suffice.
      3.2; 2, 3, 6,
      3.2; 8, 9, 11, 14, 16, 
      Hint on  8 through 16:  You should be able to tell where it is discontinuous by just thinking about the formula domain.  However, you may graph the function to decide the limit as you approach a discontinuous point.
      3.2; 24, 38.
      True or False:  The function modeling Circadian Testosterone, on p. 122; 114, is continuous everywhere.  If false, where is it discontinuous?

    • Read 3.3. (Also, do the 3.4 problems listed at the bottom.)  Remember units in applications.
      3.3; 6, 20, 25, 33, 34, 44.  You are required to follow the instructions below:
      On 20, use limit with algebra.
      On 25, use a table of values as on p. 158.
      On 34c, graph the function and get derivative from a graph tool (On TI89 graph, F5 Math, Derivative; On Desmos, can ask for f '(a)).
      3.4; 8, 9, 10.  (Since tangent line is drawn in, just take two convenient points, fairly far apart, to find slope of line.)