A Program which Permits One to "Solve" for e
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
fnInt(1/x,x, 1,D) STO> 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.
In order to make the slope of the reciprocal function equal to a log function, a base for the log function must be chosen.
There is a number to serve as a base which makes the slope of the reciprocal function equal to a log function. The ideal base is the number
that makes the area drawn at the left equal to 1. This program permits one to guess at that number, e. The number e solves the equation below
and the log used is the natural log, ln(x), loge(x).