#functions
Bot battles in graphwar, now bots can draw?? 🎨🤖 #graphwar #math #bots #ai #functions #parametric #botbattle #peacebot #larpbot How it works: 🎨 Paint Bot is the first one who doesn't fire a graph y = f(x) but a parametric curve x(t), y(t). The point moves in time t, not left to right, so the line can turn back, loop and close on itself - an ordinary function can't (one x, one y). The rose is a spiral r = 0.12 + t/16 opening over three turns, on a straight stem. The clown is 10 separate strokes with the pen lifted between them. The nose is a spiral r = 0.9·(1 − t/4π): the radius reaches zero exactly at the centre, and the centre is where Hate Bot was standing. 🪵 Log Bot fires y = 16·ln(x + 41). Its slope 16/(x + 41) drops fast: almost all the height is gained in the first few units, after that it's nearly a straight line. That's how one 11-character formula went through three bots standing at almost the same height. ⛳ Golf Bot counts characters like strokes: the shorter the formula, the better. x/9 is three characters - par. 🌀 Parametric Bot is sure he fires spirals, but he types y = ax² + bx. That's a parabola: a function can't have two y's for one x, so a loop is impossible. Spiritually, it spiralled. 😐 Larp Bot didn't fire a single shot the whole video. Just 🪵.
Peace Bot51,900 views • 2 days ago
The Fundamental Theorem of Calculus connects two main concepts in calculus: differentiation (finding the derivative) and integration (finding the antiderivative). It is split into two parts, and together they show that these two operations are essentially inverses of each other. Part 1: Taking the derivative of an antiderivative (in other words, differentiating an integral) gives back the original function. Part 2: To evaluate a definite integral (an integral that has bounds on it), find the antiderivative and plug in the top bound and then subtract from that what you get when you plug in the lower bound. KEY TAKEAWAY: The derivative and the antiderivative are opposites. #Calculus #FundamentalTheoremOfCalculus #Differentiation #Integration #MathTheory #Mathematics #Antiderivatives #RateOfChange #AreaUnderTheCurve #STEM #MathEducation #MathIsFun #MathConcepts #LearnCalculus #CalculusHelp #Mathematics #MathForEveryone #MathTeacher #MathTutorial #Functions #MathEducation #MathExplained #MathSimplified #MathTips #LearningMath #MathTutor #EducationalResources
Baddie Professor, LLC835,900 views • 2 years ago
The first key step in using the chain rule is identifying the outer and inner function. I go into this in more detail in my last video. After you kmow your outer and inner functions, find the derivative of both of them. Then plug everything into the chain rule formula. WE ARE ALL HUMANS AND ARE CAPABLE OF MAKING SILLY MISTAKES, the key is to correct yourself :-) #Calculus #ChainRule #CompositeFunctions #MathTutorial #Differentiation #MathHelp #CalculusHelp #LearningMath #MathEducation #StudentSuccess #STEM #MathProfessor #MathTutor #Tutor #MathConcepts #Algebra #MathTips #Derivatives #Mathematics #AlgebraHelp #LearnMath #MathEducation #FunctionAnalysis #MathIsFun #MathTutorial #MathExplained #STEMEducation #MathSkills #Functions
Baddie Professor, LLC625,100 views • 2 years ago
