CAS diff() giving incorrect results

09222021, 07:10 PM
(This post was last modified: 09232021 02:57 AM by Wes Loewer.)
Post: #1




CAS diff() giving incorrect results
A couple of years ago I posted about a problem with the diff() command (https://www.hpmuseum.org/forum/thread13532.html). The problem still exists in the most recent firmware.
I guess I had forgotten about the issue because I ran into the problem again yesterday, only it's worse than I original thought. The problem arises when you try to evaluate a derivative at a value, which is something that frequently comes up in calculus and physics. For instance, evaluating the 2nd derivative of x^3 at x=4. diff(x^3,x,2)x = 4 which should evaluate to 6*xx=4 which is 24. However, the CAS substitutes 4 in for x BEFORE differentiating, so the expression is interpreted as diff(4^3,4,2) = diff(64,4,2) which is meaningless. Even worse than no answer is giving the wrong answer. If the value of x contains pi, then you get incorrect results. diff(x^3+π^4,x)x = π should result in 3*x^2x=π which is 3*π^2. Instead, the line is interpreted as diff(π^3+π^4,π) and now π is treated as a variable. So the result is 3*π^2+4*π^3. This issue came to light yesterday when I was checking my test answer key and entered this (using primes which is equivalent to diff). (x^2*cos(x))''x = π evaluated to 2 instead of π^22. I assumed that I had made some silly mistake in my work by hand. It took several repeated attempts before I concluded that I was correct and the calculator was wrong. I realize I could use the d/dx template which works correctly, but there is no template for 2nd or higher order derivatives and (∂(∂(x^2*cos(x),x),x)(x = π)) looks really awkward (especially in Textbook mode) and using the ' (primes) is so very convenient. It's really an order of operations issue in which x=a should be applied AFTER the diff() command has completed, not BEFORE. And it seems only natural that the HP "Prime" should be able to correctly work with "primes". 

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Messages In This Thread 
CAS diff() giving incorrect results  Wes Loewer  09222021 07:10 PM
RE: CAS diff() giving incorrect results  parisse  09222021, 07:26 PM
RE: CAS diff() giving incorrect results  Wes Loewer  09232021, 06:20 PM
RE: CAS diff() giving incorrect results  toml_12953  09232021, 07:26 PM
RE: CAS diff() giving incorrect results  Albert Chan  09242021, 10:48 AM
RE: CAS diff() giving incorrect results  Wes Loewer  09242021, 04:28 PM
RE: CAS diff() giving incorrect results  Albert Chan  09242021, 05:23 PM
RE: CAS diff() giving incorrect results  Wes Loewer  09242021, 07:59 PM
RE: CAS diff() giving incorrect results  parisse  09252021, 04:04 PM
RE: CAS diff() giving incorrect results  Albert Chan  09252021, 05:03 PM
RE: CAS diff() giving incorrect results  Albert Chan  09262021, 12:04 PM

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