This proof should not be even called a proof. I am saying this because you assume the equation cos(x) = (e^ix + e^-ix)/2 to be true for all values of x. If I ask you to derive this equation, you would probably give me a derivation which assumes that cosine is even and sine is odd. So you are going in a loop. You assume that cosine is even because of the equation you mentioned in the video, which you assume to be true. And you assume that equation to be true because cosine is even. In mathematics, a continuous going loop is not a proof. A rigorous proof is what ends at an axiom.
Thanks for your comment! These dependencies can be subtle, and it's good to discuss them. There is a way to establish the equivalence of cos(x) = (e^ix + e^-ix)/2 without assuming cos(x) is even: establish that their Taylor Series agree term-by-term, and each have infinite radius of convergence. Where this may rely on the assumption of cosine being even is in the definition of derivative. It's worth considering more.
1. If you're on the webpage from Android Chrome, you can go to the browser menu and check the "Desktop Site" box, then everything will work like you see in this video. 2. It works similarly on iPhone Safari: www.browserstack.com/guide/request-desktop-site-on-iphone 3. If you're in the Desmos app, there isn't a clean way. You'll need to create an account, save your graph, then send it from the browser using 1 or 2. If all you need is the image, you can screenshot.
Hello! i know this video was a while ago, but what do you do if the Xor value is larger than all of the pile counts? for example, here is a game of nim: [1, 3, 5, 7, 2, 11, 13, 15, 17] the xor value of all of these piles is 26, but since no piles have 26 available, my computer cant take 26 from any pile, resulting in an error. im not sure how familiar you are with python but the code i am using to get the xor value is numpy.bitwise_xor.reduce(piles) I appreciate any help with this!
You made a mistake. It was 2.4 and not 2(4). So it should have been 2.4/2 = 1.2, but you mistook the dot for a multiplication sign and so you write 2.4/2=4. That's why you didn't arrive at your expected answer.
This conversation was very insightful; great questions and thoughtful responses that take into account the fluidity of the education model. As a university instructor I have developed a multi-faceted teaching approach that aims to engage students so they can craft the way they learn, regardless of the topic, professor, or modality. Showing students how to discover ways in which course materials can be relevant to their current lives (and their lives post-college) must go hand-in-hand with the delivery of content as a regular feature of the class experience, regardless of modality. I am looking forward to reading Dr. Talbert's book "Grading for Growth," in conjunction with his upcoming online discussion about how to reframe grading practices. Thank you Andrew for posting this interview.
Feature engineering is definitely another option. I would consider using regression with a modified set of features to still be "a different model", though.
@@octopusmath yes, I'm currently working on my self project, initially I faced this issue later I used to know about Normalize() function in preprocessing section of sklearn. This one really gave good impact towards transformation of features especially for multimodal distributed features. Now I'm getting good level of r² now. Thanks for your reply. Have a nice day👍
Why? It doesn't help with making progress, and it does the "w = x^4 +3" that started the sub process. We would need to replace w with the original function *if* we actually did an integral after substitution -- but the whole point here is that substitution doesn't help.
@@octopusmath if the anti-derivative was a composite function, as in f(g(x)), the inner function, g(x), would remain after the derivative was taken, so having g(x), x^ + 3, at the end would serve that purpose.
@@krislegends In this case what you would want at the end would be g'(x), not g(x) -- there should be a 4x^3 to cancel with the one in the denominator. There's no salvaging this one with substitution, sadly.
If you're sure it's a Caesar cipher, the thing to do is brute force. You can just try all 26 combinations, either by hand or with a computer tool. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Kn5pBG8RAUs.html
This is a topic that's typically covered in a Calculus1 course. This is a practice example for someone who understands the idea of the derivative, knows the Chain Rule formula for derivatives, and knows the derivative formula for natural log of x.
Sure, I'm always interested in seeing ciphers. It can be time-consuming to solve these and I don't really have a lot of time at the moment, but maybe others can help?
Amazing! I'm really happy I came across this video :D Edit: One thing I want to add , cause I don't think you mentioned it in the video, is that the chain rule still applies here. So: d/dx = [ sec(u)]= sec(u) tan(u) u'
