@@Goaw2551 But also a polynomial function which is in A tier. Just because your function is a special csse of another one in the list doesn't say anything about it's rating. Cubic functions are also polynomial functions and rightfully ranked very low
The example integral he showed would have broken my spirit. I don't think integration through brute force would be possible in ninety minutes for most students. Except if you're lucky and find the right substitutions first try.
same when he says that you will have an exam that if you don't score 100% you have to do it again and get a detention if you fail again until you get it right... pure pain
@@nicolasreinaldet732 Correct if you Use Lagrangian/Hamiltonian Approaches. But with Newton Mechanics you have no squares. Please correct me if I am wrong.
They deserve to be on the same tier. Parabolas are awesome, the fact that they reflect to a single point (why we use parabolic antennas), the fact that they are one of the conic curves and so much more. X^2 is definitely A tier material. But so is log(x), the fact that they convert products into adding is by itself worthy of A tier.
@@staticnullhazard6966 It will be my pleasure to interact with you on this, altought not directly correct you. Sorry for the english It Is my second language and I am still working on my speeling. Yes indead your statement Is correct, the problem Is that Newtonian mechanics Is quite a lot more limited than Its 2 equivalents. Here are the list of advantages of the other 2: Thermodinamics, and the very little Introduction to statistical mechanics I do know, are very dependent on analysing the energy function of Isolated systems and thuss are much more cosely linked to hamiltonians ( there Is even a theorem about how x^2 terms In the energy function contributed all equaly to the average energy In a linear maner for classical estatistical mechanics ). Classical ( and also quantum ) field theory Is build upon Hamiltonian and Lagrangian mechanics, and so If you want to understand complex Interactions between a atoms and light you will be using hamiltonian and lagrangian mechanics, maybe there Is a way to do field theory from newton but from my superficial contact with the area It Is always introduced with hamiltonians and lagrangians. Quantum theory foundations are entirely hamiltonian and them when you get to quantum fields you get a lagrangian option, never a newtonian analog. I am still a undergraduate so I tried my best to only speak when I knew enought about the subject, but I can also think of a few more concepts of analytical mechanics that I belive to have a better treatment using lagrangian and hamiltonian mechanics like finding conserved quantities or how the hamiltonian perturbation theory Is a more formal and cokie cut way to aproximate solutions for systems where you have a big solvable part and a smaller un-solvable perturbation. But over thosse I do not know exactly how my observations would be correct because I am still going to take analytical mechanics next semester.
@@MysteriousObjectsOfficial yes, which means they also make multiplication and division into addition and subtraction, which is fundamentally easier. It can turn all kinds of hard problems with products into subs and coefficients, which means you can apply linear algebra to the problem, then you just undo the logs at the end and you've solved it without crazy multiplication. They're also the perfect example of a group isomorphism and why they're so useful.
Analytic functions are A Tier or S tier, also sin and cos are linear combinations of e^{ix} and are so much easier to deal with once you realise this fact.
I did complex numbers for like a week in linear algebra so I didn't really get to work with them that much. What other classes would you use e^{ix} in?
@@Kcl-Integrator29 It's pretty common when solving second order differential equations, as when you get complex roots for the charecteristic polynomial, complex exponentials becomes the answer. As for when that happens in physics, is basically any time you have a oscillatory or wave like system.
@@Kcl-Integrator29 They show up in electromagnetic waves, quantum physics and computing, and for electrical engineering when finding power(The real part of the complex power at any given moment is it’s instantaneous power) using the phasor transformation.
@@theblinkingbrownie4654 No they aren't. For example f(x)=(x^4+1)/(x^2+1) is defined everywhere, thus no vertical asymptotes (for rational functions vertical asymptotes always come with undefined points at that place e.g. x/(x-1) at 1). In fact the provided f(x) doesn't have horizontal nor oblique asymptotes either since lim x->±inf of f'(x) doesn't equal 0 nor any other constant value. As far as I can tell, this is enough to show, that one particular rational function has no asymptotes. Thus you are incorrect.
I would bump trigonometrics up to S tier just because of Fourier transformation. They are huge in anything related to waves, which is almost everything.
@@SomeAndrianFirst, i don't call this abstract bullshit anymore, because the video explains it perfectly and now i know the value. Second, idk if i have or not the capacity of the aplication of maths before being in a material space were you can aply this knowledge. That is the difference of learn math in school from math in a place where you have an interest/objetives, like workplaces or field research. Third, "I doubt you have the capacity". No intention of making a personal attack, but if something is bullshit, is this fretful attitude. Not only is it a personal attack (quite cheap to be honest, come on, I'm not even attacking mathematics as an area of study), it is that it directly discourages the passion for knowing new things. Do us a favor and not replicate this in real life, *NOBODY* needs it.
The cubic function is easy to remember if you put effort. Really just a copy paste, sign switch, add the -b/3a at the end. But yeah to memorize it for the first time is daunting af
You've managed to capture what we've subconsciously felt about these functions the entire time. I agree with almost everything, except for f(x) = 1/x. He's a nice little guy and should be higher.
Logaritmic functions are S tier. You can use them for logaritmic derivation. Pretty cool properties. You can use It to adjust data to power and exponential functions with just a linear regression
Fun fact. In Ex-USSR countries squeeze theorem is called "Two policemen theorem" because you need two policemen on the each side of the drunk to transport him into jail.
Reciprocal can be cool for physics theory. Asymptotes can potentially be used for exploring black hole aspects, which is neat given that vertical asymptotes can correlate with "holes" that may represent where gravitational influence might be strong enough to create an event horizon on a 2-dimensional plane.
Honestly I kinda hate trigonometric functions because the amount of ways they can be transformed into one another just confuses me. Never know which one you're supposed to use and spend half the time trying to figure out what to do.
nah but i personally would put Rectangular hyperbolas in A tier or maybe even S , they can tell you so much about range of linear fractional functions.
bro, cubic functions are the basis for cubic splines, which allow us approximate basically any continuous function to a degree that is virtually indistinguishable by the human eye, no way they are D tier.
@@botjdjdjdif you use a Catmull-Rom spline then the factors are implicit in the data points and very simple to compute, just increase number of points until the error is acceptable
My own opinion: Constant functions:S Don’t need to explain. Linear functions(except constant functions):S Easy. Quadratic functions:D The nightmare of students in Grade 7 to 9 but it’s normal in Grade 10 to 12(I’m Grade 8). Fractional functions:B I have to find where they aren’t defined. Power functions:A They haven’t troubled me a lot. Exponential functions & logarithmic functions:C However,e^x & ln x get S. Trigonometric functions:A Beautiful functions. Inverse trigonometric functions:B They don’t appear very often. Hyperbolic functions:D I haven’t learnt them but they seem so hard. Piecewise functions(including absolute value):F It isn’t differentiable somewhere. Gamma function:A Cool. Dirichlet function:S It’s widely used as a good counter example. Composite functions:F You don’t wanna see them while differentiating.
as an engineering major, you are spot on. I would like to add that the exponential brings out a whole new world when using complex numbers and it's just the best function out there for any kind of signal processing, wavefunctions, dynamic systems, second order linear differential equations, etc.
My math professor would always joke with us about e^x Every time we go to differentiate it. He would ask “Ok what is the derivative to e^x” and us as the class would say. “e^x”. Then he would say “No the derivative of that” and we’d go on about 3-5 times before we shut up. Then next year I had him for Calc 2 so integrals. He’d ask the class ok what is the integral of e^x We’d respond e^x and he’d say no what is the integral of that. Good times I miss math class. I actually enjoyed it lmao
This is a controversial take but logarithms are both a blessing and a curse. They are a blessing because they can make certain calculations easier and sometimes when you are graphing, the relation between two variables can be more easily seen if you use a logarithmic plot. They are also a curse because certain properties make them hard to deal with. For example the complex logarithm is multi valued which is always a nuisance (it’s also multi valued in the context of Lie Groups), another annoying property is that logarithms tend to infinity but grow slower than all power functions, which is a nuisance in perturbation problems.
S tier for quadratic functions, except possibly for finding the squarefree part of discriminant: x_{1,2}=(-b+\-sqrt(b^2-4ac))/(2a) - the quadratic formula for ax^2+bx+c=0. If both roots are rational, discriminant must be a perfect square.
After Placing All the functions in the Same tier as you simultaneously I can safely say that this tier list is 'NOT' Objectively true ... It's Subjectively true
It's that really how limits are taught? Goddamn. I would teach limits with 1/x^2. Clear and simple example of a function that is discontinuous at x=0, but the limit at x=0 is clearly infinity.
I am a sciences (physics) students, and piecewise functions can actually get pretty useful in both math and physics, both as an exercice (for things other than limits, such as convergence), and as a tool. That type of function is notably used as an example of not-Riemann-integrable functions
That would be just arctan(θ)^2, wouldn't it? Since sin^2(θ)=sin(θ)^2 & cos^2(θ)=cos(θ)^2. The entire thing likely just pertains to a quirk of the notation, though.
Bro piecewise functions gave us RelU, AND Delta functions, AND methods like FEM. Sooo many uses. S++ tier. Piecewise is the protagonist who can copy others.
2:37 Dirichlet's function is actually pretty cool. Piecewise functions (especially complex/hypercomplex piecewises) are quite interesting when one (not you, obviously) understands them.
Trigonometrics are a pain in the ass. There's just too much transformations and relations you need to memorize in order to resolve some silly questions
![[TH] JFT vs RLF - VCT Ascension Pacific - Day 2](http://i.ytimg.com/vi/PuIH7w_jO6c/mqdefault.jpg)
y = e^x is the goat im glad we can all agree
Bro just _built_ like that
Yes
The real goat is y= e^-(x)^2
E is just the goat of math in general
The goat of all eigenvectors.
constant functions: S tier
all constant functions are linear functions, so yes
Constant is like y or x = num
Always has been
@@Goaw2551 But also a polynomial function which is in A tier. Just because your function is a special csse of another one in the list doesn't say anything about it's rating. Cubic functions are also polynomial functions and rightfully ranked very low
But which constant is important, they’re only really good if they don’t show up on the number line
2:21 of the professor says the exam is 1 question, then the class *SHOULDNT* be cheering
I would be terrified
better than a T/F advanced calc final
Its the school equivalent to the scene of Star Wars when the Death Star pulls up to YavinIV
The example integral he showed would have broken my spirit. I don't think integration through brute force would be possible in ninety minutes for most students. Except if you're lucky and find the right substitutions first try.
same when he says that you will have an exam that if you don't score 100% you have to do it again and get a detention if you fail again until you get it right... pure pain
As an engineer I totally agree with the S Tier choices. However, logarithm definitely scores higher than x^2.
I agree. I feel like logarithms should be A or S tier
As a physics I might add that everything Is a sprin mass system and spring mass systens are made with the x^2 function.
@@nicolasreinaldet732 Correct if you Use Lagrangian/Hamiltonian Approaches. But with Newton Mechanics you have no squares. Please correct me if I am wrong.
They deserve to be on the same tier. Parabolas are awesome, the fact that they reflect to a single point (why we use parabolic antennas), the fact that they are one of the conic curves and so much more. X^2 is definitely A tier material. But so is log(x), the fact that they convert products into adding is by itself worthy of A tier.
@@staticnullhazard6966 It will be my pleasure to interact with you on this, altought not directly correct you. Sorry for the english It Is my second language and I am still working on my speeling.
Yes indead your statement Is correct, the problem Is that Newtonian mechanics Is quite a lot more limited than Its 2 equivalents. Here are the list of advantages of the other 2:
Thermodinamics, and the very little Introduction to statistical mechanics I do know, are very dependent on analysing the energy function of Isolated systems and thuss are much more cosely linked to hamiltonians ( there Is even a theorem about how x^2 terms In the energy function contributed all equaly to the average energy In a linear maner for classical estatistical mechanics ).
Classical ( and also quantum ) field theory Is build upon Hamiltonian and Lagrangian mechanics, and so If you want to understand complex Interactions between a atoms and light you will be using hamiltonian and lagrangian mechanics, maybe there Is a way to do field theory from newton but from my superficial contact with the area It Is always introduced with hamiltonians and lagrangians.
Quantum theory foundations are entirely hamiltonian and them when you get to quantum fields you get a lagrangian option, never a newtonian analog.
I am still a undergraduate so I tried my best to only speak when I knew enought about the subject, but I can also think of a few more concepts of analytical mechanics that I belive to have a better treatment using lagrangian and hamiltonian mechanics like finding conserved quantities or how the hamiltonian perturbation theory Is a more formal and cokie cut way to aproximate solutions for systems where you have a big solvable part and a smaller un-solvable perturbation. But over thosse I do not know exactly how my observations would be correct because I am still going to take analytical mechanics next semester.
4:21 trig is both a blessing and a curse
Bro just saied nothing
They cancel like x/x
I abhor Trigonometry x Mathematical Induction crossover. I can't even prove P(1) is true with all the convoluted trigonometric conversion.
Yeah thats fair @@nothingbutpain863
trig is so annoying especially with the Fourier series, I hate it with my everything
i never in my life though i would see functions tier list
Yet here it is. The function waited for us to get pain acknowledged by us
Logarithms are S tier. Literally make huge multiplications into puny additions.
Whole vid is spot on except logarithm which is straight S
but they make subtraction and addition into division and multiplication like log(100) - log(10) = log (100/10). and log (10) + log(10) = log(100)
@@MysteriousObjectsOfficial yes, which means they also make multiplication and division into addition and subtraction, which is fundamentally easier. It can turn all kinds of hard problems with products into subs and coefficients, which means you can apply linear algebra to the problem, then you just undo the logs at the end and you've solved it without crazy multiplication.
They're also the perfect example of a group isomorphism and why they're so useful.
I need more math shitposting in my life
same fam
Okbuddyphd
glad you choose not to trigger every engineering grad PTSD with Heaviside and Dirac functions
Why did the Dirac function fail it’s driving test?
It couldn’t stay within the limits. 😎
I think those are classified as distributions, they are not well-defined functions.
@@forthehomies7043 ahh yes the dad jokes that are actually funny
Isn't the Heaviside function just a shifted sgn?
@@themachine9366 Heaviside is a perfectly defined function, one of the simplest ones
The goat e^x every engineer’s favorite because you never have to calculate it, just leave it as is.
S tier - simple functions
B tier - Borel measurable
C tier - Riemann integrable
D tier - Lebesgue integrable
F tier - the rest
🤓
@@probasteelchiquitoahorapro1490🤡
It's been a while since I've brushed up on my measure theory, but S, B and C are all lebesgue integregrable aren't they? So they're also in D
A-tier: Analytic/smooth functions (depending on personal taste)
(Also, all tiers implicitly exclude the previous tier.
where tf a functions
for whatever reason my mental image of the e^x function is a chill looking dude with sunglasses smoking a massive blunt
"BEAT HERE" 💀
“BEAT HERE”
Non-elementary functions:
S tier
@@АннаСивер-г8м😮😮😮
S Tier for basically the same reason as Complex Numbers. Just built like that and I respect it.
Bro made cubic dirty, it could just be a part of the polinomial equations
Cirno do you do well in Math class
@@fireblazenotbulgaria3053that's Aqua in their pfp but they're both dummies and related to water so you get a pass
At least they have a closed form for roots
cause cubic functions are in general useless. at least high degree polinomial can be used to approximate functions
This is the kind of nerd content I'm glad to see in my recommendations, thank you
Analytic functions are A Tier or S tier, also sin and cos are linear combinations of e^{ix} and are so much easier to deal with once you realise this fact.
I did complex numbers for like a week in linear algebra so I didn't really get to work with them that much. What other classes would you use e^{ix} in?
@@Kcl-Integrator29 It's pretty common when solving second order differential equations, as when you get complex roots for the charecteristic polynomial, complex exponentials becomes the answer. As for when that happens in physics, is basically any time you have a oscillatory or wave like system.
analytic and numeric solutions to PDEs. fourier transform
@@Kcl-Integrator29 complex analysis
@@Kcl-Integrator29 They show up in electromagnetic waves, quantum physics and computing, and for electrical engineering when finding power(The real part of the complex power at any given moment is it’s instantaneous power) using the phasor transformation.
As a math teacher, I laughed when you said peice wise are only used for teaching limits Becuase that’s the truest thing I’ve ever heard 😭💀
My tier list (with some functions added)
S: Linear, e^x
A: Quadratic, Logarithm, Trigonometric, Gaussian (Bell Curve) Distribution
B: Polynomial, 1/x, Gamma Function (Extension of Factorial)
C: Square Root, Absolute Value, Inverse Trig
D: Cubic, Rational Function, n-th Root, Floor/Ceiling
F: Piecewise, Hyperbolic Trig
Placements based on usefulness and simplicity
Logarithmic functions not being s tier is an absolute crime.
Engineers watching this video: 🥳
High school students:
My teacher letted us use calculator in the exam and i discovered by myself how to calculate the opposite of a trig
Rational functions with no asymptotes are S tier too ngl.
*no vertical asymptotes
Arent they just polynomials then
@@theblinkingbrownie4654 No they aren't. For example f(x)=(x^4+1)/(x^2+1) is defined everywhere, thus no vertical asymptotes (for rational functions vertical asymptotes always come with undefined points at that place e.g. x/(x-1) at 1).
In fact the provided f(x) doesn't have horizontal nor oblique asymptotes either since lim x->±inf of f'(x) doesn't equal 0 nor any other constant value. As far as I can tell, this is enough to show, that one particular rational function has no asymptotes. Thus you are incorrect.
@@Foxxey oh right i forgot that the denominator can have no real roots lol
Good luck with arctangent lol
3:35 missed opportunity for literally any domain expansion meme
DOMAIN EXPANSION: COMPLEX NUMBERS
I would bump trigonometrics up to S tier just because of Fourier transformation. They are huge in anything related to waves, which is almost everything.
The Fourier transform is actually a type of Laplace transform which makes use of, you guessed it, e^ix. Which is already rightfully in S Tier.
As a person more interested in human sciences, i think this is very cool finally knowing the applications of what some day i called "abstract bs".
you can't perform any kind of science without understanding data, which requires math.
No, you don't know the applications of what you call "abstract bs"
I doubt you have the capacity
@@SomeAndrianFirst, i don't call this abstract bullshit anymore, because the video explains it perfectly and now i know the value.
Second, idk if i have or not the capacity of the aplication of maths before being in a material space were you can aply this knowledge. That is the difference of learn math in school from math in a place where you have an interest/objetives, like workplaces or field research.
Third, "I doubt you have the capacity". No intention of making a personal attack, but if something is bullshit, is this fretful attitude. Not only is it a personal attack (quite cheap to be honest, come on, I'm not even attacking mathematics as an area of study), it is that it directly discourages the passion for knowing new things. Do us a favor and not replicate this in real life, *NOBODY* needs it.
@@SomeAndrian ok Terrence Tao
@@muralibhat8776
Terrence Tao is doing mostly pure math.
Thanks for playing
You know what is amazing about trigonometry func. once you achieve the eq. in cos or sin you will get very near to range
Complex numbers: 🗿
the partial derivitive. Awesome going forward. A nightmare undoing them
that’s an operator, not a function
@@thegoofiestgoooberrur mom is an operator and not a function
@@NotBroihon T_T why u bully him?
@@extreme4180 because im evil 😈😈😈
@@thegoofiestgoooberran operator is definitionally a function
e^x is S+. not only is it cool af like u described but its super useful for casual real world problems
also seems clear to me you have definitely encountered maths from an applied perspective. im chill with it but biased af
I was gonna say this tierlist was bad. But then I realised it is objectively correct. Have a good day.
Non-elementary functions S+ infinity
Non-quadrature functions: SS+ tier 💀
The cubic function is easy to remember if you put effort. Really just a copy paste, sign switch, add the -b/3a at the end. But yeah to memorize it for the first time is daunting af
2:21 imagine having everything correct in the question but you forget to put the +C
probably the tier list i most agree with. Piercewise may be dumb, you only need one, but they are really good at explaining limits and discontinuities
You've managed to capture what we've subconsciously felt about these functions the entire time. I agree with almost everything, except for f(x) = 1/x. He's a nice little guy and should be higher.
He put logarithms in B tier and thought we wouldn't notice.
I was subconsciously waiting for this!
y=x : "Who are you? "
y=x²/x : "I am you, but discontinued at 0"
Edit: I guess it's working for all y=(x^n/x^(n-1)), n ≥ 2
interesting ...
y=x³/x² entered chat
@@melonenlord2723
Don't bring the [y=(x^n/x^(n-1), n ≥ 2] family 💀
@@mazmuz987 x^(1/2) / x^(-1/2) 💀
trig for sure the hardest thing for me to memorize but really rewarding
we have math function tier list before GTA 6 lol
Logaritmic functions are S tier. You can use them for logaritmic derivation. Pretty cool properties. You can use It to adjust data to power and exponential functions with just a linear regression
As a wannabe engineer who has his eng school admission exams this week, this should help with the integral area problem questions
Fun fact.
In Ex-USSR countries squeeze theorem is called "Two policemen theorem" because you need two policemen on the each side of the drunk to transport him into jail.
You did logarithms dirty - they're so important in engineering and are like e^x's twin
Here I am procrastinating on studying for my math exam by watching people rank math functions.
Reciprocal can be cool for physics theory. Asymptotes can potentially be used for exploring black hole aspects, which is neat given that vertical asymptotes can correlate with "holes" that may represent where gravitational influence might be strong enough to create an event horizon on a 2-dimensional plane.
Honestly I kinda hate trigonometric functions because the amount of ways they can be transformed into one another just confuses me. Never know which one you're supposed to use and spend half the time trying to figure out what to do.
nah but i personally would put Rectangular hyperbolas in A tier or maybe even S , they can tell you so much about range of linear fractional functions.
"Very beautiful, very powerful"
This is all very valid except logarithmic functions deserve a b tier and not a c tier
This video might be based on a lot of personal grief, but it seems very fair
bro, cubic functions are the basis for cubic splines, which allow us approximate basically any continuous function to a degree that is virtually indistinguishable by the human eye, no way they are D tier.
Good luck finding their factors
@@botjdjdjdif you use a Catmull-Rom spline then the factors are implicit in the data points and very simple to compute, just increase number of points until the error is acceptable
@@API-Beast I haven't read cubic functions at that level, i am a high school sophomore
In the world of computing you can just use bezier curves or trilinear interpolation instead of cubic splines.
My own opinion:
Constant functions:S Don’t need to explain.
Linear functions(except constant functions):S Easy.
Quadratic functions:D The nightmare of students in Grade 7 to 9 but it’s normal in Grade 10 to 12(I’m Grade 8).
Fractional functions:B I have to find where they aren’t defined.
Power functions:A They haven’t troubled me a lot.
Exponential functions & logarithmic functions:C However,e^x & ln x get S.
Trigonometric functions:A Beautiful functions.
Inverse trigonometric functions:B They don’t appear very often.
Hyperbolic functions:D I haven’t learnt them but they seem so hard.
Piecewise functions(including absolute value):F It isn’t differentiable somewhere.
Gamma function:A Cool.
Dirichlet function:S It’s widely used as a good counter example.
Composite functions:F You don’t wanna see them while differentiating.
as an engineering major, you are spot on.
I would like to add that the exponential brings out a whole new world when using complex numbers and it's just the best function out there for any kind of signal processing, wavefunctions, dynamic systems, second order linear differential equations, etc.
A good first math course list! Would love to the step function and the dirac function aswell. They are quite interesting.
I used trig functions to make the Last Prism (terraria weapon) in Minecraft, so yeah, circles also.
Trig and power functions must be at the S tier man you feel me :') without them there is no fourier transform or taylor expansion
My math professor would always joke with us about e^x
Every time we go to differentiate it. He would ask “Ok what is the derivative to e^x” and us as the class would say. “e^x”. Then he would say “No the derivative of that” and we’d go on about 3-5 times before we shut up.
Then next year I had him for Calc 2 so integrals.
He’d ask the class ok what is the integral of e^x
We’d respond e^x and he’d say no what is the integral of that.
Good times I miss math class. I actually enjoyed it lmao
This is a controversial take but logarithms are both a blessing and a curse. They are a blessing because they can make certain calculations easier and sometimes when you are graphing, the relation between two variables can be more easily seen if you use a logarithmic plot. They are also a curse because certain properties make them hard to deal with. For example the complex logarithm is multi valued which is always a nuisance (it’s also multi valued in the context of Lie Groups), another annoying property is that logarithms tend to infinity but grow slower than all power functions, which is a nuisance in perturbation problems.
Piecewise functions are really useful in transfer functions/systems and signals!
2:24 imagine doing all of that just to forget the + c (constant of integration)
I agree with almost everything 👍
Maybe 2 or 3 I would put a rank below or above, but I would have done the exact same tier list apart from those 👌
S tier for quadratic functions, except possibly for finding the squarefree part of discriminant: x_{1,2}=(-b+\-sqrt(b^2-4ac))/(2a) - the quadratic formula for ax^2+bx+c=0. If both roots are rational, discriminant must be a perfect square.
2:10 they found the values for a b c, so inefficiently, could just put it into reduce row echelon form using linear algebra or a calculator
Piecewise functions are really useful in transfer systems and signals!
Constant algebraic functions S+ tier
Trig fluctuates between S tier and F tier with great frequency
You would think that you are done linear algebra in 9th grade, but nothing can prepare you for the horrors that wait post-secondary linear algebra.
After Placing All the functions in the Same tier as you simultaneously I can safely say that this tier list is 'NOT' Objectively true ...
It's Subjectively true
I never thought I'd enjoy this video as much as I did
This is actually outstandingly correct tier list
imagine a calculus question with e^f(x) where f(x) is a function in x
Therapist: ignore the intrusive thoughts
*intrusive thoughts*
half angle indentities
Calculus tier list
U sub: S tier. Trig sub: F tier.
derivatives: S tier
anti derivative: b tier
@@Kcl-Integrator29trig sub is my favorite integration technique by far :(
This was basically a calc tier list
This man really put the cubic function in D tier, 😂. WHO LET BRO COOK?!
Sending this to my Math Teacher
Linear Function is the Goat 🗣🔥
i remember rudin calls e^x ‘the most important function in mathematics’ (and therefore everything). euler formula really is a gem
f(x) = |x| being C tier is the most relatable thing in the world. Sometimes is a blessing and sometimes is a pain in the ass.
It's that really how limits are taught? Goddamn. I would teach limits with 1/x^2. Clear and simple example of a function that is discontinuous at x=0, but the limit at x=0 is clearly infinity.
Logarithms are definitely S tier, they are so useful
I am a sciences (physics) students, and piecewise functions can actually get pretty useful in both math and physics, both as an exercice (for things other than limits, such as convergence), and as a tool. That type of function is notably used as an example of not-Riemann-integrable functions
we need arctan2, the ultimate dual-parameter function
That would be just arctan(θ)^2, wouldn't it? Since sin^2(θ)=sin(θ)^2 & cos^2(θ)=cos(θ)^2. The entire thing likely just pertains to a quirk of the notation, though.
0:52 (X-13) (X+17)
Bro piecewise functions gave us RelU, AND Delta functions, AND methods like FEM. Sooo many uses. S++ tier. Piecewise is the protagonist who can copy others.
2:37 Dirichlet's function is actually pretty cool. Piecewise functions (especially complex/hypercomplex piecewises) are quite interesting when one (not you, obviously) understands them.
0:08 "linear" "1/2 x + 8" you had one job
That is a linear equation
Thats linear
@akshatmodi8607 @@mashucha no, that's affine
You and 6 other people are incredibly stupid.
"Cubic D tier" algebraic geometers wanna to know you location
Babe wake up new math functions tierlist just dropped 🗣️🗣️🔥
I was game for this until my man basically put Bézier in D-tier
As someone in pre calculus logs are F just because they make no sense im failing that unit only
tbh x/(x^5+1) integral is not as bad, you just can be lost at dividing it to smaller fractions
bro that limit at the end ☠️
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it's actually easy to solve well starting with : for whatever value to X form R : 0
Trigonometrics are a pain in the ass. There's just too much transformations and relations you need to memorize in order to resolve some silly questions
"If you see a polynomial while integrating, it can be a blessing"
Sure honey, integrate 1/(x⁵+1)
I understand that the function isn't a polynomial but technically you are seeing a polynomial while integrating
Rational: Please make the decision to ignore these functions when possible. That's a Smoove move indeed
ok, this is the best tier list ever made
Logarithmic deserves s tier because of the slide rule
I believe logarithmic functions are the same as exponential ones though.