A Program which Permits One to "Solve" for e
Students who have never studied series or compounding have little background for e, the base of the natural log.
This program gives them an introduction without series, compounding, or calc.
In order for the integration to work nicely,
a base for the log function must be chosen. There is a number to serve as a base. The ideal base is the number that makes the area drawn at the left in red equal to 1.
This program permits one to guess at that number, e. The number e is the base of the natural log, ln(x), loge(x).
The calculator program shades the requested area under the curve and completes the computation seeking
an area or result equaling 1. See the box at the left.
- 1st. Store 1/x in Y9 in the Y= menu.
- You may turn off the equal sign if you wish so the function stays stored and not visible in your other graphs.
- 2nd. Store the following program in the calculator. Locations of key functions and constants are found below.
- Disp "Y9 is 1/x"
- -.5 STO> Xmin
- 5 STO> Xmax
- -.5 STO> Ymin
- 5 STO> Ymax
- 1 STO> Xscl
- DrawF Y9
- Input "e?",D
- fnInt(1/x,x, 1,D) STO> E
- Disp E
- 3rd. Run the program.
- 4th. At the first pause the above image is shown without the shading.
- 5th. Press [Enter] to continue with the program.
- 6th. A prompt next requests the guessed solution. Enter the guess.
- 7th. The requested area is shaded and computed.
- 8th. Enter another quess or e as desired.
- 9th. When you are finished with the program use ClrDraw to clear your graphing screen.
- ClrDraw, DrawF, Line, and Shade are found in the Draw menu.
- Xmin, Xmax, Ymin, and Ymax are found in the Var, Window menu.
- fnInt is found in the Calc menu above Trace.
- Shade(lower,higher, leftX,rightX,patterns,patres) and its parameters.
- fnInt(expression,variable, lower,upper,[tolerance]) and its parameters.
- Line(x1,y1,x2,y2) and its parameters.