Checking input doesn't work for exponential expression because of big numbers?

I’m working on an activity to generate infinite practice problems for integration formulas. I am generating a lot of random parameters, and checking for the difference between the student’s entered expression and the correct antiderivative evaluated at a few different values.

It was going fine until I added an exponential expression, lol. Now when I check at even a moderately large-ish value, it does not give me a “correct”. As long as I only check at very small values, it seems to work OK. I assume this has something to do with the algorithms and how super-ginormous numbers are handled? Or rounding??

Is there any way to fix this? I mean, I think it will be fine if I just use the small-value-check-points. But I’m really curious now.

Here is the activity, with SMALL check values in screen 1 and LARGE-ish values in screen 2. Pay no attention to the “troubleshooting” note, this is still very much a work in progress, lol.

We use multiple checkpoints. 3 check points for most expressions. at 1.1, 2.1 and 3.1 as long as they are in the domain and have not had issues

Right. I know it will work if I use smaller numbers. In this case, even 3.1 is too large though. From some trial and error, I need to my checkpoints to be in about the 0-2 range at most.

I know how to fix it. I’m mostly curious about why it happens and how I can know exactly when I need to “keep check values small”, and how to know the parameters as to what is “small enough”.

I had a similar issue with large numbers in an activity. Try displaying in the note what the “correct” answer should be to help troubleshoot. When I did this, I noticed the number would switch to scientific notation in the note around 21 digits and wouldn’t match the correct answer. This may still be true, but this was last spring and it may have changed since then.

Yeah, it definitely has something to do with sci notation, I think. I do have a troubleshooting note, but the “correct” answer isn’t numerical, it’s an expression. I’m giving students a function and having them find an antiderivative. Then the “check” uses the derivative of their submission and checks it against the original function, evaluated at a few values and totaled up. Then I check THAT value to be <0.001.

It works fine until I have an exponential expression in the answer, and then even with a small-ish checker value (like 3) the difference can some out huge. I guess I’ll just stick with smalllll values for the check and test run a few times to make sure it’s working properly.

I made this activity it works for most functions. Maybe it could help!

Students type in a function and then they check to see if they can find the antiderivative.

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That’s pretty cool! I see that it does have the same issue, though. The “breaking point” seems to be around 18x in the exponential…

Yeah I see what you mean. Here I adjusted evaluations and I was able to check up to 178!


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