AB Calculus: RAM Day 1
1. The table below shows the velocity of a model train engine moving along a track for 10 sec. Estimate the distance traveled by the engine using:
Time(sec) / Velocity
(in/sec) / Time
(sec) / Velocity
(in/sec)
0 / 3 / 6 / 11
1 / 12 / 7 / 6
2 / 22 / 8 / 2
3 / 10 / 9 / 6
4 / 5 / 10 / 1
5 / 13
a) LRAM with 10 subintervals.
b) RRAM with 10 subintervals.
c)MRAM with 5 subintervals.
2. You are walking along the bank of a tidal river watching the incoming tide carry a bottle upstream. You record the velocity of the flow every 5 minutes for an hour, with the results shown in the table below. About how far upstream does the bottle travel during the hour?
Time(min) / Velocity
(m/sec) / Time
(min) / Velocity
(m/sec)
0 / 1 / 35 / 1.2
5 / 1.2 / 40 / 1
10 / 1.7 / 45 / 1.8
15 / 2 / 50 / 1.5
20 / 1.8 / 55 / 1.2
25 / 1.6 / 60 / 0
30 / 1.4
a) Find the LRAM estimate using 12 subintervals.
b) Find the RRAM estimate using 12 subintervals.
x / 1 / 1.75 / 2 / 2.5 / 3f(x) / 4 / 12 / 6 / 12 / 2
3. Given the data below estimate the area under the curve using four subintervals. Note: the lengths of the subintervals are not equal.
a) LRAM
b) RRAM
4. Using the graph below, estimate the area under the curve for
a) the interval [0, 8] using LRAM with eight subintervals.
b) the interval [0, 9] using RRAM with three subintervals.
c) the interval [0, 8] using MRAM with four subintervals.