not your AVERAGE Putnam limit (2021 Putnam A2)
Вставка
- Опубліковано 25 чер 2022
- not your AVERAGE Putnam limit. We evaluate a limit with exponential functions and averages, taken from the William Lowell Putnam Math Competition. This is problem A2 from the 2021 Putnam exam. We do this by taking logarithms, hospital’s rule, derivatives of exponential functions, and the definition of e as a limit. This is a must see for calculus 1 students and anyone interested in math Olympiad problems, enjoy!
YT channel: / drpeyam
TikTok channel: / drpeyam
Instagram: / peyamstagram
Twitter: / drpeyam
Teespring merch: teespring.com/stores/dr-peyam
your vids are such fun, great vibes sir.
Basic stuff but interesting. Especially the use of the l'Hospital rule (not very intuitive...). Thank you Dr Peyam.
Love the little Mohawk
also... GREAT VIDEO!
saw this ahter 14 secs it was loaded
awesome !
@@diniaadil6154 thanks!
i did it slightly different- first i took ln(g(x)) as you did, but then i didn't use de"hospital rule- instead i used inequality y/(y+1)
There is a mean value theorem trick for this one, when I saw this problem in a forum thread a while ago. Sadly I was stumped by most of the other problems, maybe I got one of the others right? But Real Analysis 1 is one of my strongest areas. A difference of two things with a "+c" inside the parentheses once suggests MVT!
A slight change, but I had to save the limits for the end and define (g(x,h))^h = (x+1)^(h+1) - x^(h+1).
This is equal to f(x+1) - f(x) = f'(x*), for some x* in (x,x+1), where f(x) = x^(h+1). So g(x,h)^h = (h+1)x*^h, and g(x,h) = (1+h)^(1/h)*(x*). x*/x is in the interval (1, 1+1/x), so you can take the limits as h to 0 and x to infinity in that order with a bit of squeeze theorem thrown in.
nice!!
i like this
Does the logistic map recurrence relation have a closed form?
That smile @ 5:00 😆😆😆
This was a fun one!
LMAO , that mic🎤 drop at end 🔚 😂😂😂
yessir
شكرا على معلومات 🙋♀️🙋♀️🙏🙏🙏🙏👈👈👈👈🔔🔔🔔👍👍😥😥😥😥🙏🙏🙏🙏
Hello Dr. Peyam, just to let you know, your title is wrong. It should be Question A2. Question A1 is about the grasshopper, which I actually solved over on my channel. It's also a not-to-hard question involving vectors and 3-4-5 right triangles, somewhat easy for a Putnam. Looks like 2021 was an easy year, relatively speaking.
Your solution by the way is elegant and your explanation is great. As you say, a Calc 1 student can do it if he knows what to look for.
Thanks!!
Sir do you teach at any University?
We're 4D. Like quaternion math.
I keep hearing theories like "simulation", "holographic" or back to Leibniz' "contingent" universe.
Those theories all match the i, j, k in quaternions.
Quaternion
MATHEMATICS
a complex number of the form w + xi + yj + zk, where w, x, y, z are real numbers and i, j, k are imaginary units that satisfy certain conditions.
RARE/biblical
a set of four parts, things or persons. (dimensions?)
L'Hôpitalizable...
😁😁😁😁😁😁
3 sets of 3 dimensions.
1D, 2D, 3D are spatial
4D, 5D, 6D are temporal
7D, 8D, 9D are spectral
1D, 4D, 7D line/length/continuous
2D, 5D, 8D width/breadth/emission
3D, 6D, 9D height/depth/absorption
Doctor! Please show some respect and do proper hornes)))), not some spider man ))))
Hahaha