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In-Class Activities for MTH 201 Calculus Module 1A

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In-class activity set for GVSU MTH 201 Fall 2020 Module 1A (finding instantaneous velocity)

In-Class Activities for MTH 201 Calculus Module 1A

  1. 1. MTH 201: Calculus Module 1A: How do we measure velocity? Prof. Talbert GVSU July 22, 2020
  2. 2. Agenda for today Review of Daily Prep assignment, and Q+A
  3. 3. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity
  4. 4. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view
  5. 5. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view Further practice with the concept
  6. 6. Agenda for today Review of Daily Prep assignment, and Q+A Activity: Going from average velocity to instantaneous velocity Minilecture: What this means from a graphical point of view Further practice with the concept For next time: Followup activities and things to do
  7. 7. Polling for today Go to www.mentimeter.com and enter code xx yy zz
  8. 8. A basic question Reminder The average velocity of a moving object is an estimate of its velocity over an interval of time. The instantaneous velocity of a moving object is its velocity at a single moment in time. Fundamental Question It’s easy to find average velocity given two points. But how do you find instantaneous velocity, where you only have one point? Activity: On your device, go to the spreadsheet set up at: https://bit.ly/201-1a
  9. 9. Debrief with a graph https://www.desmos.com/calculator/obpytdzxsf
  10. 10. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)).
  11. 11. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached.
  12. 12. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero.
  13. 13. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero. It’s also the slope of the “tangent line” that touches the graph of s(t) at the single point (a, s(a)). If we zoomed in on the graph of s at this point, the graph would flatten out at appear to be equal to this line.
  14. 14. Summing it up The average velocity of an object on the interval [a, b] is the slope of the “secant line” that goes through (a, s(a)) and (b, s(b)). To find the instantaneous velocity of the object at the single time value t = a: Move the second point b closer to a, measure the average velocity, and repeat – look for a single value that is being approached. Alternate take: Think of the second point b as a + h where h is a small distance, and let h move toward zero. It’s also the slope of the “tangent line” that touches the graph of s(t) at the single point (a, s(a)). If we zoomed in on the graph of s at this point, the graph would flatten out at appear to be equal to this line.
  15. 15. Applying the concept Back to Mentimeter for two polling questions
  16. 16. NEXT TIME... Followup activities: To be done on your schedule, posted to ClassKick (watch CampusWire and Blackboard for a link). Complete by due date for 1 engagement credit. Daily Prep for Part B: Go ahead and start reading/watching video; see calendar for due date Ask questions and interact: Get on CampusWire and share thoughts, questions, and help.
  • ChuckJackson1

    Sep. 4, 2020

In-class activity set for GVSU MTH 201 Fall 2020 Module 1A (finding instantaneous velocity)

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