Jim Doherty

@KarenCampe This was shown to me by one of my colleagues. I have to admit I have never thought of applying FTC this way, but with our notation on integrals going to the left instead of right, I think this makes some sense

@mrdardy Hmmmm...

An interesting take on the FTC from a student at our school. Asked for the derivative of the integral of sqrt (t) from 4 to x^2, she identified three cases for the answer. A) 2 < |x| B) 2 = |x| C) |x| < 2 Is she overthinking it, or have I been underthinking FTC?

Trig question : for f(x) = A cos (bx) + C sin (dx) I know that the period is the LCM of the two component periods. Is there a way to find the amplitude? Is amplitude a logical question?

Tonight's show on wrkc.kings.edu is uploaded Here - mixcloud.com/DJCalc/dj-calc… and here - djcalc.com/2025/12/16/dec… Spotify Link - open.spotify.com/playlist/0hfF3… Playlist

@dmarain David can you give me some insight into why the (8-x+1)*(8 - y +1) formula gives me the number of x by y rectangles on the chessboard?

@mrdardy outstanding discovery work! Now ask him to write the formula for an mxn chessboard!😊😊😊

In Calc BC yesterday I posted a picture of a chessboard and asked for how many squares there would be. We worked our way through to the answer. I then posed the question of how many x by y rectangles there would be. One student proposed (8-x+1)*(8-y+1) 1/2

@dmarain He proposed one! (Sum of 1 to m (sum on 1 to n (m-x+1) (n- y + 1)) for rectangles of dimension x by y.

A quick check seems to confirm this. Are these formulas ones any of you have seen before? He could not really explain his insight comfortably. 3/2

His formula seems to check. Someone else then asked about the number of rectangles is the original size was not 8 by 8 but, instead, an m by n rectangle. My student who proposed the original formula thinks this is a sum of sigma 1 to m of (m-x+1) and sigma 1 to n of (n-y+1) 2/2

Tonight's show uploaded here - djcalc.com/2025/12/02/dec… and here - mixcloud.com/DJCalc/dj-calc… Spotify Link - open.spotify.com/playlist/54zht… Playlist

Tonight's show uploaded here - mixcloud.com/DJCalc/dj-calc… and here - djcalc.com/2025/11/18/nov… Spotify Link - open.spotify.com/playlist/05lWa… Tonight's Playlist

Tonight's show uploaded here - mixcloud.com/DJCalc/dj-calc… and here - djcalc.com/2025/11/11/nov… Spotify Link - open.spotify.com/playlist/0ougp… Tonight's Playlist

For my show tonight on wrkc.kings.edu (7 - 9 PM ET) I shine a spotlight on The Bats (new album!) and feature @voxtrot @nadasurf @AmyRigby and new tunes by @cuddlemagic , Melody Chambers, Bruiser and Bicycle, and 16 others. You can stream from our site, so drop on by!

@HarMath @dmarain Fred - thanks for the reply. I am trying to remember where I found this question or what I was thinking when I assigned it. What tip could I give to my students about thinking of the 75th term?

@mrdardy @dmarain One possible series: + 13, + 3, + 23, + 3, + 33, + 3, + 43, ... Neither in this case 24, 37, 40, 63, 66, 99, 102, 145, 148, 191, . . .

@HarMath @dmarain I wrote a HW problem and I cannot remember what I was thinking when I wrote it! Consider the sequence: 24, 37, 40, 63, 66, ... a) Is this arithmetic, geometric, or neither? b) Is 189 in the sequence? c) What is the 75th term in the sequence? Any elegant ideas?

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@HarMath @dmarain @howie_hua @decompwlj @RaminKhosravi4 @sonukg4india @jamestanton @mATH_e_matics @MathCurmudgeon @pickover Wild guessing here looking for a generalization. 13/999 is repeating 13 in base 10 (9 is one less than 10) 21 repeating in base 3 is 21/22 (2 is one less than 3) How about something like 23 repeating in base 4? Is it 23/33 (3 is one less than 4) ?

@dmarain @howie_hua @decompwlj @RaminKhosravi4 @sonukg4india @jamestanton @mATH_e_matics @MathCurmudgeon @pickover I saw the 4-digit 1001 pattern which = 1001/1111 in binary. Converting this back to decimal = 9/15 or 3/5 In decimals, anything over 9's repeats. 0.135 all-repeating = 135/999 = 15/111 = 5/37 0.21 all-repeating in Base 3 would be 21/22 in Base 3

Consider the following infinite repeating 'decimal' in base 2: 0.100110011001... (a) Convert it to p/q in base 10 Method? (b) Questions suggested by part (a)? @HarMath @howie_hua @decompwlj @RaminKhosravi4 @sonukg4india @jamestanton @mATH_e_matics @MathCurmudgeon @pickover

@HarMath @dmarain @howie_hua @RaminKhosravi4 @mathillustrated @mATH_e_matics @decompwlj @ybgoi @sonukg4india @jamestanton @DonFraser9 @dment37 This is a lovely and clear solution to this problem. I am curious about how long it would take some of my AP Precalc students to arrive at this solution. I think the biggest hurdle is simply writing the equation that represents the description

@dmarain @howie_hua @RaminKhosravi4 @mathillustrated @mATH_e_matics @decompwlj @ybgoi @sonukg4india @jamestanton @DonFraser9 @dment37 And once a class makes this discovery, how many verifications will they need to do to believe their hypothesis?

The sum of the reciprocals of two positive numbers is four times the reciprocal of their sum. Relationship between the numbers? Explain. @HarMath @howie_hua @RaminKhosravi4 @mathillustrated @mATH_e_matics @decompwlj @ybgoi @sonukg4india @jamestanton @DonFraser9 @dment37

It has been too long since I checked in on this account and it has been way too long since I blogged about my classes. Hoping to get more engaged again and here is my starting salvo mrdardy.mtbos.org/2025/10/21/upd…

@martinsean As with most things, it was filled with pros and cons. It took me awhile to adjust my pace of speaking and remind myself to be careful with math vocab. I am looking forward to seeing these kids grow in our school after years of just getting to know jrs and srs

@mrdardy How did it go??

Hey #mtbos I will be teaching Algebra I this coming year for the first time in quite a while. Can you send me or share some favorites for this level course? I've been teaching Calc and Precalc for the past 6 years exclusively