(09-20-2023 07:07 AM)Matt Agajanian Wrote: [ -> ]Hi all.
...do you see the CW having any merits, applications, benefits?
Here's a novel 991CW application: manual iteration to solve a transcendental equation using the 991CW's composite functions.
The simple looking transcendental equation, e^-x = x, is unsolvable in closed form (try it!). While easy to solve using a graphical calculator by plotting both the LHS and RHS and finding their intersection, equations such as this can also be solved by iteration, e.g., selecting a value for x, calculating e^-x (which becomes the new value of x), rinse and repeat, with the values, if plotted, forming a cobweb plot.
An iterative solution can be found using a spreadsheet like Excel or Google Sheets that permits circular references by selecting the iteration option and limiting the number of iterations (to prevent infinite loops). However, I've not found a calculator spreadsheet (including the 991CW spreadsheet) that allows circular references.
On the 991CW one can use manual iteration via composite functions to work around the circular reference issue, and without a spreadsheet, as follows:
1) From Home, highlight Calculate, click EXE and click Function.
2) Highlight Define f(x), enter e^-x, and click EXE.
3) Click Function, highlight Define g(x), click EXE, click x, and click EXE.
4) Click Variable, highlight x, enter 0.5 as an initial guess, click EXE.
5) Click Home, highlight Calculate, click EXE, click Function, highlight f(x) and complete "f(" by clicking "x" and entering ")" to get "f(x)" and select EXE.
The first iterate 0.6065306597 is displayed. To manually obtain subsequent iterates, the steps are simply as follows.
6) Click Variable, highlight x, click EXE, highlight STORE, click EXE, and the first iterate becomes the new value of x.
7) Click EXE again to update the value of f(x) and obtain the 2nd iterate: 0.5452392119
8) Repeat steps 6 and 7 to obtain the remaining iterates.
The first 12 iterates (sufficient to achieve convergence to within 0.001) are as follows (if no transcription errors).
1) 0.6065306597
2) 0.5452392119
3) 0.5797030949
4) 0.5600646279
5) 0.571172149
6) 0.564862947
7) 0.5684380476
8) 0.5664094527
9) 0.5675596343
10) 0.5669072129
11) 0.567277196
12) 0.5670673519
Wolfram Alpha gives the solution as 0.567143.