1. USE A COUPLE OF DIFFERENT RAMS AND LET’S SEE IF THE ‘ONE TRUE ANSWER’ DOESN’T EMERGE.

2. ‘AREA’ AS AN EMERGENT PROPERTY (LRAM SIDE) N (# of columns) Type: L or R RAM? ResultN (# of columns) Type: L or R RAM? Result

3. ‘AREA’ AS AN EMERGENT PROPERTY (RRAM SIDE) N (# of columns) Type: L or R RAM? ResultN (# of columns) Type: L or R RAM? Result

4. IN WORDS, THE INTEGRAL (CALCULATION OF AREA) IS THE AREA THAT EMERGES AS WE LET THE N  ∞. THE VALUE, THE AREA, ‘EMERGES’ REGARDLESS OF THE CHOICE OF MODEL!

5. NEW TASK: THE VELOCITY OF A MODEL PLANE IS GIVEN BY V(T) = 2LN(T + 1) + 8, WITH T IN SECONDS AND VELOCITY IN METERS/SECOND. Use the process we outlined: through a series of estimates, make a prediction for the “area under the curve” in the first 10 seconds.

6. IN CASE WE DON’T TALK ABOUT DURING CLASS: 1. Quiz on calculator prowess Monday 2. Also on the table work we do next. 3. The “area” from that last slide is really DISTANCE 4. It comes with units: meters

7. I DRIVE A HONDA CIVIC SI. ROAD AND TRACK ANALYZED THIS CAR A FEW YEARS AGO AND FOUND THESE CHARACTERISTI CS: timeSpeed 00 0.610 1.520 2.430 3.740 550 6.860 8.770 11.280 13.990 17100 na110

8. HOPEFULLY, I REMEMBERED TO ASK YOU WHAT THE UNITS WERE, WHAT WAS GOING ON, ETC. LET’S USE THIS PAGE TO KEEP TRACK OF THOSE ANSWERS

9. BY THE TIME THE CAR IS MOVING AT 100MPH, 17 SECONDS HAS ELAPSED. HOW FAR AWAY IS THE CAR?

10. BACK TO THE DATA TABLE: ENTER THE DATA INTO YOUR LISTS; LET’S CONVERT TO FEET / SECOND (THERE ARE 5,280 FEET IN A MILE AND 60X60 SECONDS IN AN HOUR – LET’S USE A LITTLE DIMENSIONAL ANALYSIS) timeSpeed 00 0.610 1.520 2.430 3.740 550 6.860 8.770 11.280 13.990 17100 na110

11. TAKE L2 X 5280 / 3600 AND STORE IT IN … L2 YOUR NEW VALUES COMPARE SECONDS FROM START TO FEET PER SECOND

12. AT THIS POINT, IT GET HARD TO RUN CLASS FROM A POWERPOINT…. BUT I STILL WANT TO KNOW: HOW MANY “FEET” HAS THE CAR MOVED? time seconds speed in ft / sec 00.000 0.614.667 1.529.333 2.444.000 3.758.667 573.333 6.888.000 8.7102.667 11.2117.333 13.9132.000 17146.667 na161.333