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CASIO fx-CG50 question - lrdheat - 01-05-2020 05:49 PM
A list of solutions from SolveN of d/dx of a function of interest was generated. I want to then take this list, and plug it into the function of interest. How is this accomplished? A plus would be to produce a table of the function values at the solutions produced but SolveN of d/dx.
RE: CASIO fx-CG50 question - Mjim - 01-07-2020 01:18 AM
When you use SolveN it stores the list in the variable List Ans, which is like the Ans variable but for lists. [OPTN][F1][F1] to type List, [SHIFT][(-)] to select Ans. You can then pretty much use it directly (note that the derivative isn't typed as it appears on the Casio for simplification purposes):
SolveN((sinx)'=1, x, 0, 20pi)
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
cos List Ans
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
Of course this updates the List Ans variable so you need to store it first if you wish to use it again:
SolveN((sinx)'=1, x, 0, 20pi)
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
List Ans -> List 1
cos List Ans
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
List 1
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
List Ans
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
There are 26 available list variables (1-26). In addtion Lists can be addressed with square brackets to extract values (index starts from 1):
List 1
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
List 1[5]
8pi
List 1[1]
0
Another useful function is Seq accessed by [OPTN][F1][F5] which allows you to create function tables directly without having to jump into the table mode:
seq(<function>, <function variable>, <start>, <stop>, <interval size> )
You can use the List addressing to input the list values from the output from the SolveN function like entering cos directly above:
SolveN((sinx)'=1, x, 0, 20pi)
{0, 2pi, 4pi, 6pi, 8pi, 10pi, 12pi, 14pi, 16pi, 18pi}
List Ans -> List 1
seq(cos List 1[x], x, 1, 10, 1)
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
I don't know all of the functions myself, but Casio is pretty good with handling lists. You can for example take an input list in pounds and output a list in kg using the unit convertor, without having to input each value individually.
RE: CASIO fx-CG50 question - lrdheat - 01-07-2020 11:13 PM
Thanks, good information.
I am still having difficulties. I used SolveN(d/dx (x^2 (x+1)^3 )/((x-2)^2 (x-4)^4) and got 5 zeroes (4 are mins or maxes, 1 is an inflection). As you stated, this goes into List ans. I have the equation that I applied d/dx stored in the graph app as Y15. How do I evaluate Y15 using the List ans?
The graph of Y15 can be plotted and analyzed over a domain of, say, -25 to 10, and it produces max and mins at the same numbers produced by SolveN. I cannot figure out how to produce the max/mins using List ans.
RE: CASIO fx-CG50 question - lrdheat - 01-08-2020 02:40 AM
I figured this out! By going into table app, and then set up, by choosing the list that I saved List ans to, table now displays my function for the zeroes of d/dx of my function!
This is quite a nice capability!
Thanks again!
RE: CASIO fx-CG50 question - lrdheat - 01-08-2020 02:42 AM
The opportunity to choose the list that I wish to enter in table is accomplished in the table set up option “Variable”.
RE: CASIO fx-CG50 question - Mjim - 01-08-2020 11:17 AM
Seems that I learned something as well.
I had no idea that you could use previously saved lists instead of creating a custom range. Thanks for sharing (and for your third post clarifying where to find the toggle in table mode).
I don't know if this is of any use to you, but you also have a "Function Memory" that is able to store up to 20 formula's when the Input/Output mode is set to Linear in Run-Matrix mode.
The nice thing is that the Casio saves both the Math and Linear mode history so you can switch between both at will (the individual histories for both modes are retained even on power off). In this way you can store formulas created in linear mode and paste them into math mode, and the paste functionality will convert automatically between VPAM/Natural Textbook or vice-versa depending on what mode you paste the formula in.
The copy and paste functionality also works in different modes, so you can take a formula you created in table mode, copy it, switch to Run-Matrix mode, switch to Linear input mode, paste the formula, then store it in one of the 20 function memories for use later. Weirdly, the copy functionality doesn't work in Table/Graphing mode if you are in Linear mode, so you need to be in math mode to copy formulas to the clipboard, which you can then paste in Run-Matrix mode in either Math/Linear mode. You can of course copy formulas from Run-Matrix mode into Table/Graphing mode, just make sure that Table/Graphing mode is set to Math mode before pasting (Disclaimer: I just tested this myself, so I may have overlooked something here).
RE: CASIO fx-CG50 question - lrdheat - 01-08-2020 03:15 PM
Nice!
I wonder why CASIO did not include a fuller complex number capability (ASIN 2 throws an error). No factorization of numbers into it’s prime constituents. Can’t use min or max of multiple functions in an analysis, just min or max of a set of numbers. Also, with integrals, will usually have difficulties with infinite endpoints or within the domain being considered (requiring breaking integral into multiple integrals, and adding or subtracting 1 E-12 from offending endpoints).
Otherwise, quite an impressive device!
RE: CASIO fx-CG50 question - Mjim - 01-08-2020 11:14 PM
Well it's not really Casio, but you can get around some of those weaknesses by installing Khicas for the Prizm:
https://www-fourier.ujf-grenoble.fr/~parisse/install_en#casio
I'm not an expert on the software, but it seemed to handle ASIN(2):
asin(2)
(-i)*ln(2*i+i*sqrt(3))
Also works with large prime factors:
ifactor(987654321)
3^2*17^2*379721
Seems fine with improper integrals (admittedly, that is about the extent of my knowledge, so there might be some things it can't do):
integrate(1/x,x,0,1)
+infinity
Though using a third party program may not be ideal, this app alone is one of the primary reasons I purchased the fx-CG50. It is more limited than Xcas from what I hear (something about squeezing it into a 2MB file size), but having a nicely featured algebraic CAS system for free is pretty awesome.