Short and Sweet Math Challenge #1

[DA74254]

Well, so far, the WP43 deems this equation [#5] being too complex - it shouldn't do so, however, IMHO. Filed as an issue in GitLab already.

... and solved today thanks to Mihail. Next release of WP43 will allow handling such expressions as well.

Thank you. Looking forward to next release that I can crash

[dm319]

Looks like my DM42 needs a new battery judging by the apple core in the top corner. So this is me naively plugging this into plus42 instead.

[*] cos(x)*ln(x) from 0 to 1,

-0.9461

[*] 1/√x from 0 to 1,

2

[*] ln(Γ(x)) from 0 to 1,

I have no idea what that symbol is. Googling brings up the gamma function, but I am still as lost.

0.9189

[*] 1/√(-ln(x)) from 0 to 1,

1.7724

[*] e^(x+sin(e^(e^(e^(x + 1/3))))) from -1 to 1, and

2.9944

[*] sin^2 (tan(tan(π x))) from 0 to 1.

0.3911

[dm319]

Please completely ignore what I've highlighted.

My midldle kid when he gets angry, his face goes dark and he yells at anyone looking at him with "Stop Looking At ME!!!". I've tried to explain many times that yelling tends to attract attention, but have so far failed.

[Walter]

Looks like my DM42 needs a new battery judging by the apple core in the top corner. So this is me naively plugging this into plus42 instead.
...

Thanks for participating. Can you produce some digits more, please?

[rawi]

A new solution with HP Prime G2 (all results showed up immediately; only task 6 took a few seconds):
1. -0.946083070367
2. 2.000000000000
3. Error message "invalid input."
4. 1.77245374158
5. 4.317536556730
6. 0.390529009507

A comparison of these results with the solution of the DM32 and additionally with the solution given by the TI 89 Titanium:
1, 2, 4, and 6 showed the same or nearly identical solutions as the DM32.
3 Does not have a solution with the HP Prime but has a solution with the DM32. The TI 89 Titanium cannot compute it because it does not have the Gamma function.
5: The DM32 solution and the HP Prime solution differ significantly. The TI 89 Titanium gave the same solution as the HP Prime.

[dm319]

Thanks for participating. Can you produce some digits more, please?

You asked so nicely so

1. -0.946083070364651469787517137915227
2. 1.999997984972843300762957296036196
3. 0.91893853320214119662649529540602
4. 1.772451835878367295522711550526266
5. 2.994395690716520827680123994800296
6. 0.391051754591745341017960523894429

If I have some time this evening I'll try the DM42.

[dm319]

Used a website to visualise some of the plots.

Here are 1-4:

Screenshot at 2023-11-20 18-47-08.png (45.77 KiB) Viewed 302 times

Here are 5-6:

Screenshot at 2023-11-20 18-47-42.png (31.77 KiB) Viewed 302 times

[dm319]

DM42, with ACC setting.

1. e-5
-0.99998042078

2. e-5
1.99998387978

3. e-6
0.91893836727

4. e-4
1.77232488922

5. e-2
3.25179953247

6. e-10
0.00000000009310338

Not sure what's going on with 6.

[Walter]

What about the times your calculator needs to compute your results? And ACC=1e-2 isn't really ambitious, is it? Why do you need all those many pretty digits then?

[dm319]

Why do you need all those many pretty digits then?

So you can tell me exactly how wrong it is!

ACC was carefully adjusted to allow a similar computation speed which was less than a long time and longer than a couple moments.

PS, does anyone integrate on their calculators, and why?