1. Applications of RAM
Section 5.1b

2. (a) Estimate distance with LRAM:
The “Do Now” – p.255: #10
Time
(sec)
Velocity
(in/sec) 20 1 2 3 4 5 6 7 8 9 10 12 22 10 5 13 11 6 2 15
Velocity (in/sec) 10 5 1 2 3 4 5 6 7 8 9 10
Time (sec)
(a) Estimate distance with LRAM:
1( )
= 87 in
= 7.25 ft

3. (a) Estimate distance with RRAM:
The “Do Now” – p.255: #10
Time
(sec)
Velocity
(in/sec) 20 1 2 3 4 5 6 7 8 9 10 12 22 10 5 13 11 6 2 15
Velocity (in/sec) 10 5 1 2 3 4 5 6 7 8 9 10
Time (sec)
(a) Estimate distance with RRAM:
1( )
= 87 in
= 7.25 ft

4. Estimate for road length using LRAM:
Now let’s work through #12 on the same page!!! 50 40 30
Velocity (ft/sec) 20 10 10 20 30 40 50 60 70 80 90
100
110
120
Time (sec)
Estimate for road length using LRAM:
10( … + 30)
= 3490 ft

5. Estimate for road length using RRAM:
Now let’s work through #12 on the same page!!! 50 40 30
Velocity (ft/sec) 20 10 10 20 30 40 50 60 70 80 90
100
110
120
Time (sec)
Estimate for road length using RRAM:
10( … + 35)
= 3840 ft

6. Now let’s work through #12 on the same page!!!50 40 30
Velocity (ft/sec) 20 10 10 20 30 40 50 60 70 80 90
100
110
120
Time (sec)
3490 ft ft
Average =
= 3665 ft 2

7. Using RAM to Approximate Volume
Estimate the volume of a solid sphere of radius 4.
First, graph the function:
Now, imagine the sphere as the
revolution of this function about
the x-axis…

8. Using RAM to Approximate Volume
Estimate the volume of a solid sphere of radius 4.
We partition the function into
8 subintervals of equal length
and slice the sphere with planes
perpendicular to the x-axis at the
partition points.
Look at the diagrams on p.251…

9. Using RAM to Approximate Volume
Estimate the volume of a solid sphere of radius 4.
Each slice can be approximated
by a cylinder:
Height:
Radius:
Volume of each cylinder:

10. Using RAM to Approximate Volume
Estimate the volume of a solid sphere of radius 4.
Use the RAM program:
Function:
Interval: [– 4, 4]
Number of Slices (n)
MRAM n 10 25 50
100
Let’s work with this last value…

11. The error percentage is only about 5 thousandths of a percent!
Using RAM to Approximate Volume
Estimate the volume of a solid sphere of radius 4.
Approximated volume:
How close is this to the actual volume?:
The error percentage is only
about 5 thousandths of a percent!
As a percentage of V :

12. Using RAM to Approximate Volume
Let’s try #20 on p.256…
Volume of each of the cylinders:
Use LRAM with on the interval [0,5], n = 5: