Sect 2.5, #20, Investigating discontinuities from a Piecewise Function

[@Silver_G]

I realize that my University-level Calculus book received from my best friend is the exact same book as mentioned in the description… he gave me for free! Just because he doesn't need it anymore (he is not math major) and I want to dive into Calculus! What a good friend he is =]

[@blackpenredpen]

Indeed : )

[@cycklist]

You're the best, Steve. It's been a privilege to watch the amazing growth of your channel.

[@blackpenredpen]

Portsmouth FC thank you so much, friend!

[@DarkMage2k]

Makes me really happy to see that his channel is getting more recognition. I hope he reaches to level of Numberphile or other maths channel fast

[@blackpenredpen]

Dark Mage thank you.

[@busta5384]

His name's Steve?

[@gergodenes6360]

Lovely video. I have a quite interesting problem that you might enjoy solving: find the local maxima and the global minima of the function e^x-x^e. For an advanced level, find all global and local maxima and minima for a^x-x^a, in which a is a real number. Hope you'll see this and have fun! Cheers!

[@blackpenredpen]

Thank you. That's a nice problem and it is somewhat similar to my vid on x^y=y^x. : )

[@travishayes6037]

As as Master's Student in Mathematics at UCLA, I want to say you are a better teacher than most of the graduate student teachers here. You'd be a great professor (if you're not already).

[@abhay7280]

Helps me for these type of questions.. thumbs up for this guy.😁

[@anuradha9283]

this guy is a beauty at teaching math! excellent work steve!

[@keshavgoyal571]

Maths may not teach me how to Add love or Subtract hate but it gives me hope that every problem has a solution.

[@darnellyiadom3596]

That's a really cool t-shirt, maybe you could make a few more copies and sell it

[@EsubalewHabtie-nt7zt]

Keep it up teacher

[@SeriousApache]

0:46 you probably meant x ≠ 1

[@blackpenredpen]

RUSapache yes. I said it wrong.

[@helloitsme7553]

Maybe a cool question if you have a piecewise function with a constant c in it, which constant c will make the piecewise function continuous?

[@VaradMahashabde]

The shirt is great, but it would be better if all the formulae were for me in an exam and not the guy behind me #yay

[@hamiltonianpathondodecahed5236]

U could just gift this shirt to the guy in front of u. #yay#lol

[@DarkMage2k]

Great video as always, mate! Really love the explanation, where you make maths look really fun :) By the way, I'd love to see a video on graphical transformations as new operations are done on a given function, just like you did for the shifting of 1/x+1 due to it being negative and addition of 1. #YAY

[@tareqabuelkomboz3912]

First👀No but for real, great video as always✌🏼

[@milos_radovanovic]

While you'r on a subject of continius functions, removable discontinuitis, and picewise functions, can you do a video on a 1-D "Bump function" (y=exp(1/(1-x^2) for |x|

[@milos_radovanovic]

Also it is quite interesting case for limit of an infinitely differentiable function, and rich topic of distributions!

[@milos_radovanovic]

Or perhaps, have a Dr. Peyam do it?

[@kerPlanck]

Nice video! By the way, in terms of good exercises, which book is better, Stewart or Larson? Thanks!

[@DDW-ig3mz]

How do you solve this problem by using numerical approach

[@MuhammadAli-gn4hx]

Brilliant

[@Lklibertad]

Hello :) nice video I have a question about Max of f(min(x1,x2,...,xn)) when f(x) it's a function of min(x1,x2,...,xn)

[@alwysrite]

very nice !

[@rareclassix7589]

Before simplifying the function when x=1 it is undefined as you end up with 0/0. How can f(1) without the piecewise element therefore be 1/2 ?

[@golfchan3613]

I'm no expert, but I think that it's because it appears to be multipled by x-1, instead of some term multiplied by x, so when x is not 0 there is some possibility of encountering a problem with 0 when if it was 0 it would be fine. In this case, the problem arrives when we are at 1.

[@soumyachandrakar9100]

#yay

[@diabloa.1700]

YAY

[@zorak0044]

Hi! Please HELP me with this problem: If g is continuous and f is not continuous. Is it possible that the quotient f/g, been a continuous function? Proof the answer. I realy hope you can help me w this one!

[@arequina]

I'll take a XXL for that shirt, please.

[@atharvsawant7509]

How do you solve the limit as x->0 ((tan(x))^3-(tan(x^3)))/x^5 without repeatedly using L'Hospital rule?

[@gurvishwassingh5542]

Just use tanx/x=1 as limit x tends to zero you will get 1/(x^2)-1/(x^2) and we get 0/(x^2) so it is 0 because any number except zero divided by 0 is zero because x is tends to zero not equal to zero and we get tanx/x=1 from series of tanx or by dividing series of sinx/cosx . So in conclusion answer is zero.

[@calcul8er205]

You still get an indeterminate form (0/0) using the tanx/x limits, it seems that there’s is more work involved. Using a graphing calculator it seems that the limit approaches 1

[@gurvishwassingh5542]

Calcul8er how 0/(x^2) is all what we get and that is just zero you can show that by using l'hospital rule.

[@atharvsawant7509]

attyfarbuckle Thanks! The series expansion worked. The answer comes out to be 1.

[@coolity163]

how can i get such shirt

[@helloitsme7553]

Coolity he'll do a give away and I think he'll also sell them

[@staswisniewski4101]

If i am from poland can i win tshirt?

[@jamieee472]

51st

[@artey6671]

Looks like you made the same mistake again. If f(-1) is undefined, it can't be discontinuous there.

[@artey6671]

Basically, yeah. If a function isn't defined at some value, you don't really say that it's discontinuous there.