Continuous, Discontinuous, and Piecewise Functions

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We know a lot about functions now, so let's look at some special cases where functions get weird and jump around.
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Опубликовано:

30 сен 2024

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Комментарии : 87

@yogeshdharshan9588 5 лет назад

Your intro song was soo funny, it's like retro cartoon song

@amjadhossain4901 3 года назад

You are one of the best mathematics teachers l have seen ever. Your videos are too helpful for the students like us.We get immense help from your videos.These videos make our topics quite easier.Carry on.

@rik9833 3 года назад

Your intro and outro reminds me of some old educational cartoon I use to watch when I didn't go to school as a child. I love that vibe

@beyondartists7641 3 года назад

Well detailed explanation. Wasted 3 hr trying to understand my professor 😒

@PeakOfPeace 3 года назад

There is a lot of intensity in your voice, your words directly go into my head.😄

@longlostwraith5106 3 года назад

Sorry professor, but I disagree with 2:55 . 0/0 is not undefined, it is indeterminate. Not the same. 0/0 can actually be anything we want, as any real number can be the solution to the equation "0x = 0". Therefore, since "(x-1)/(x-1)" CAN be 1 for all real values including 1, it can be safely simplified without having to exclude 1. If I'm wrong and you have the time to explain this to me, please do.

@manaarikicarpentier6038 2 года назад

Nope, you can't do 0/0 simply because you can't divide by 0 because this implies that 0 has an inverse which is false. Because if there's an x such that 0x = 1 that's absurde because for all x, 0x = 0. so for all x, x/0 is undefined in particular, 0/0 is undefined. We talk about indeterminate when we are dealing with limits (which we were not in this case)

@longlostwraith5106 2 года назад

@@manaarikicarpentier6038 No, sorry, you are utterly wrong about this.

@manaarikicarpentier6038 2 года назад

@@longlostwraith5106 why?

@longlostwraith5106 2 года назад

@@manaarikicarpentier6038 Because "0x = 1" and "0x = 0" are two completely different beasts. In the first one, "x" can't be any real number. In the second one, "x" can be any real number you want it to be.

@manaarikicarpentier6038 2 года назад

@@longlostwraith5106 exactly, you can't find any x such that 0x=1 so 0 isn't inversible thus you can't divide by 0

@Alpha-bz6ke Год назад

Great tutorial. I completely understood continuous and discontinuous with just one explanation.

@CartoonKidOLLY 2 года назад

3:05 that was totally you scratching your beard

@propaulplays9062 2 месяца назад

😩

@eternal___official Год назад

2:45 - so... (x^2-1)/x-1 = x-1 but x cannot equal 1 for the first case but CAN be 1 for the second case of function. Wouldn't that mean that we are "wrong" when we say (x^2-1)/x-1 = x-1??? i'm confused...

@mansanasmdelf0759 5 лет назад

Thabk you so much!!! This helps me a lot

@mubeenkhan6131 3 года назад

Sir please make a lecture on how a discontinuous function is converted into a continuous function with the use of unit step function.

@WeSoldOurLives 4 года назад

Thank you professor Dave!

@physics_enthusiast_Soorya 2 месяца назад

Any function with a vertical asymptote must be a "Continuous" function, according to my textbooks.. My teacher told me that they will never meet, but that doesn't mean there's a gap, they'll meet at infinity.

@algorithme1950 Месяц назад

Yes this videos is wrong

@leetoka2292 3 года назад

Thank you professor dave! Liked and subbed

@pripsshorts0516 2 года назад

Can someone please explain me the example of piecewise function..i didn't get how the coordinates (-2,5) and (-2,-3)were found .

@vodiact Год назад

do you still need help

@Butterfly-bs7jp Год назад

@@vodiact please explainnn 🥺

@vodiact Год назад

@@Butterfly-bs7jp actually i have no idea now

@lunes-1 3 года назад

📚great video,keep it up!

@alburnto 5 лет назад

Dave, isn't the function 1 / x - 1 not graphed as it should be? For example, if you plug x = 2, y gives back 1, and the coordinate (2, 1) is not in the curve.

@ProfessorDaveExplains 5 лет назад

hmm yeah it's not perfect, the asymptotes are correct but it's not a flawless representation. i don't really have a way to get the curves perfect as i just paste them together from a stock image of a parabola or something, please excuse the approximation!

@alburnto 5 лет назад

@@ProfessorDaveExplains totally excusable :) Thanks for your work!

@ashutoshtiwari3785 4 года назад

@@ProfessorDaveExplains You should use Manim if you know Python for visualisations.

@tino_ 2 года назад

MR PROFESSOR DAVE THANK YOU SO MUCH I DONT KNOW WHAT I WOULDVE DONE IF IT WERENT FOR YOU THANK YOU AGAIN

@WilhemHohenzollen Месяц назад

i mean f(x)=5 when x

@sarathkumar4504 4 года назад

Sir can u give me any application of discontinuity in science

@christinejoyceballos2076 4 года назад

OMG THANK YOU SO MUCH GOD BLESS YOU

@Nishantmakadiya 3 месяца назад

I am literally Speed running mathamatics🏃💨

@miguelcielos9442 3 месяца назад

Bro's locking in

@sue4552 2 месяца назад

do you understand how the thing became -3?

@AlessandroZir 2 года назад

thank you!! very clear and intuitive; you do know how to teach;

@nikocvitanic7701 3 года назад

bro that's about as simple as it gets. you're a fucgggging G

@jonykhan4395 8 месяцев назад

Good explanation. If a function is discontinuous then why we call it A FUNCTION ANYMORE? it is in the definition of a function that its all domain members MUST have unique image But one of the domain members does not have value then Why call it a function?? If the function is producing Irrational numbers then is it a continuous or discontinuous? if a function outputs Infinity it will be a continuous or discontinuous? if a function outputs a non-terminating value it will be a continuous or discontinuous? if a function outputs indeterminate forms type values is it a continuers or discontinuous?

@karam3045 3 года назад

Never seen a better teacher

@AhmadNour 3 года назад

very helpful ♥

@ummahyehmmm7403 3 года назад

Thanks for saving me again!

@Stoirelius 4 года назад

At 3:00 how would I know 1 is not a value if I was just seeing the simplified function of x +1??

@ummehabibahappy2161 4 года назад

if we put value 1 for x then it will undefined that's why here 1 cant be the value of x..

@heydrianluisanilao1757 2 года назад

Then x + 1 is the only thing you have to be concerned about

@charblaze1231 3 года назад

Thanks

@ThWRizzler 3 месяца назад

W you remind me of my younger days in elementary school but for harder math!

@sameedansar3552 2 года назад

Thank you🌟

@bryanjaviercancejo 3 года назад

Thank you Sirrrr

@alexandroskourtis5268 Год назад

THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU

@abdurrahmansembiring5862 3 года назад

thank you professor

@ankitasaxena9724 3 года назад

Very helpful

@atullizard5219 2 года назад

2:17 can this function be called piecewise function?

@deloriadaniellemariea8184 3 года назад

Thank you!!

@isabellawilliams52 2 года назад

super helpful!

@pranavsblog9782 5 лет назад

Your a great teacher amazing exmalantion

@SamuelCarlton_ 4 года назад

Life saver

@anmolkotiyal6272 3 года назад

The way he Explains.... Like puts effort in his voice..... I get it Totally.... Humble guy 😄

@willdompert3422 5 лет назад

you are Jesus christ

@timothymcglynn1935 Месяц назад

Thanks 👍

@medotedo8410 4 года назад

so most rational functions are discontinuous functions

@claressalatia 3 года назад

Hello Professor Dave. At 2:54, how would i know that x cannot be equal to 1 if it shows only the simplified function?

@BankBlitz818 3 года назад

Then you won't have to worry about it. :)

@anishpalabatla4543 3 года назад

The function is (x^2-1)/(x-1) by default hence, 1 is a point of discontinuity. But, if the function is x-1, there is no restricted domain, i.e x€R. Hope this helps you :)

@heydrianluisanilao1757 2 года назад

Then x + 1 is the only thing you have to be concerned about

@cometolearn8598 2 года назад

because if x is equal to 1 then we get x^2 - 1/1-1 which here 1-1 makes the denominator = to 0 meaning the function will become undefined and the function would be discontinuous Hope this helped :)