100 calculus limits (ft epsilon-delta definition and Riemann sum limits )

[@blackpenredpen]

If you spot any mistakes, please comment below and I will add them to the description later. Thank you!

[@edwardhuang5885]

idk if anybody has spotted this already but at 7:13:23 the numerator of the final term should have been "n" not "n^2"

[@tambuwalmathsclass]

GOAT

[@jozhaoyuansong6937]

Could you add the question 42 please? I can't solve it without using the l'hopital's rule. Thanks !!

[@0123vegeta]

Not sure if mistake or I'm wrong. But question 39. Arccos(sqrt(3)/2). Isn't it +π/6 and -π/6 So D.N.E? Great video btw!

[@aaaaaa-rr8xm]

I was just watching your 100 integrals video

[@codyriceandothers]

everyone's impressed that you can solve 100 limits in one take, but I'm impressed how you can stand up for 7.5 hours straight

[@blackpenredpen]

That’s called being a teacher. 😆

[@YoavZilka]

@@blackpenredpen we stand with you teachers. Pun intended

[@jeremygodoy18]

nothing beats manual.

[@j.m.8895]

And holds the microphone for 7+ straight hours.

[@asilbek5727]

@@blackpenredpen You are literally the best teacher to learn math from. Better than all the professors I know

[@nocturnalvisionmusic]

*this calculus master ain't got no limits* 😎🥳

[@PovertyBench]

Nah you just gotta use L’Hopital’s rule and you’ll find the limit

[@nocturnalvisionmusic]

@@PovertyBench :)

[@good-luck-ugo]

Yo, that's a sick comment

[@nocturnalvisionmusic]

@@good-luck-ugo aww yeah thank you! 🥰

[@tatamata515]

Next 100 differential equations

[@user-wu8yq1rb9t]

I'm agree 👍

[@soumalyaghosal3854]

Yeah🔥

[@Nutshell_Mathematica]

Agree too

[@musiclofi3789]

Yeah man

[@mcalkis5771]

Bruh you'll get the man killed. A differential equation can take like 10-20 minutes to solve.

[@stephenbeck7222]

Yes this is right in the middle of my Calc BC class. We will just watch this instead of having class (we are working on limits anyway!).

[@blackpenredpen]

Your semester starts already?!

[@stephenbeck7222]

@@blackpenredpen high school in the south. Some places started august 1st

[@blackpenredpen]

@@stephenbeck7222 that’s so early!

[@integrationmaster]

@@blackpenredpen Mine's Already Started Too!

[@super9296]

@@blackpenredpen very early indeed.

[@blackpenredpen]

Big thanks to Abby for helping me with the timestamps! [Q1 to Q10] use the graph Q1, 0:48 Q2, 7:26 Q3, 13:16 Q4, 17:29 Q5, 22:01, limits of sin(x)/x Q6, 26:46 Q7, 34:32 Q8, 38:45 Q9, 49:11 Q10,52:55, limit of tan^-1(x) [Q11 to Q20] Limits from piecewise functions Q11,57:25 Q12,1:00:31 Q13,1:04:29 Q14,1:09:11 Q15, 1:13:20 Q16, 1:16:21 Q17, 1:19:40, limit of abs(x)/x Q18, 1:23:10 Q19, 1:26:59, limit of the floor function, floor(x), aka the greatest integer function Q20, 1:32:33 [Q21 to Q35] limit as x goes to a, do not use L'Hospital's Rule Q21, 1:35:29, factor & cancel Q22, 1:38:38 Q23, 1:41:54, use the conjugate Q24, 1:45:31 Q25, 1:49:01, expand Q26, 1:53:05, just plug in Q27, 1:55:09, factor the sum of two cubes Q28, 1:58:28, polynomial long division or synthetic division Q29, 2:04:45, simplify the complex fraction Q30, 2:07:50 Q31, 1:12:34 Q32, 2:17:08 Q33, 2:22:08, multiply the lowest common denominator Q34, 2:24:57, factor x-8 as a difference of two cubes Q35, 2:28:45, use the conjugate [Q36 to Q45] limits at infinity Q36, 2:32:59 Q37, 2:34:36 Q38, 2:35:58 Q39, 2:41:49 Q40, 2:43:23 Q41, 2:45:08 Q42, I accidentally skipped this... Q43, 2:47:22 Q44, 2:50:38 Q45, 2:55:04 [Q46 to Q55] definition of derivative in terms of the limit Q46, 3:02:36 Q47, 3:08:48 Q48, 3:13:08 Q49, 3:16:32 Q50, 3:19:44 Q51, 3:25:42 Q52, 3:32:40 Q53, 3:35:36 Q54, 3:41:51 Q55, 3:49:56 [Q56 to Q70] L'Hospital's Rule Q56, 3:56:06 Q57, 4:05:28 Q58, 4:13:40 Q59, 4:16:25 Q60, 4:20:40 Q61, 4:22:49 Q62, 4:25:25 Q63, 4:28:33 Q64, 4:34:05 Q65, 4:37:22 Q66, 4:40:02 Q67, 4:41:24 Q68, 4:43:56 Q69, 4:49:41 Q70, 4:55:20 [Q71 to Q80] my limit secret weaspons Q71, 5:02:21 Q72, 5:04:54 Q73, 5:06:55 Q74, 5:08:09 Q75, 5:09:03 Q76, 5:14:34 Q77, 5:15:35 Q78, 5:17:26 Q79, 5:22:15 Q80, 5:24:12 [Q81 to Q90] the epsilon-delta definition of a limit Q81, 5:26:27 Q82, 5:35:55 Q83, 5:41:03 Q84, 5:45:05 Q85, 5:51:54 Q86, 5:56:46 Q87, 6:05:02 Q88, 6:10:37 Q89, 6:18:45 Q90, 6:24:49 [Q91 to Q100] limit as integrals (Riemann Sum) Q91, 6:32:37 Q92, 6:44:34 Q93, 6:52:59 Q94, 6:57:20 Q95, 7:04:06 Q96, 7:08:39 Q97, 7:10:09 Q98, 7:11:25 Q99, 7:13:30 Q100,7:19:00

[@atomspalter2090]

thanks for the timestamps

[@IlIlllIlll]

Hello BPRP

[@octopuskeng]

I am so excited to watch this video!

[@atomspalter2090]

@@octopuskeng same

[@integrationmaster]

Can't Wait :))

[@ngrm]

You're my hero man. As an aspiring math educator, I see this level of dedication as a force of nature.

[@ralphhebgen7067]

Wow. I am seriously impressed. 7.5h standing up straight, maintaining mental focus, and explaining things lucidly. The only thing I have ever done for that long without a break is sleeping… 🤘👍

[@showtimemaster1824]

He is a math menace! Someone give this man a raise!

[@tambuwalmathsclass]

You are doing absolutely an incredible work, I'm just Imagining how possible I can talk for 7 hours 😲 May God bless you more 💪

[@blackpenredpen]

Thank you so much 😀

[@du42bz]

Can you prove the existence of your imaginary god?

[@Francesco-ib7dx]

4:54:45 we can factorise the same way we did with the limit of x approaching 0+ and we get: lim x--> infinity (24x^7)/(64x^7 - 24x^4) = lim x--> infinity 24/(64 - 24/x^3); substitute infinity and we get 24/64 = 3/8 5:16:35 we can rewrite as e^ (lim x-->infinity(x^2ln(1-1/x))) We can use l'hospital rule for the limit if we rewrite it as lim x -->infinity (ln(1-1/x)/1/x^2) then we get lim x -- > infinity (1/x^2 -x)/(-2/x^3) adjust the fraction and simpliy: lim x --> infinity (x^2/(-2x+2)) this is just negative infinity so we have e^negative infinity which is 0 by the way keep doing this its amazing and i don't know how you can stay focused for 7 and a half hours straight.

[@chennebicken372]

Love, how you make so much maths accessible to everybody. This is so valueable for „normal“ people but also so practical for people who study mathematics. ❤️❤️❤️

[@yashyadav602]

broo like I am not even a calc student yet but I fricking love this vids... I solve all these integrals with you... Thanks for being so awesome

[@blackpenredpen]

Thanks. I am happy to hear it 😃

[@Cm-zc2zx]

Kis class me ho bro?

[@colleen9493]

@Yash Yadav that was me a few years ago, you’ll love calculus.

[@mathmancalc7753]

You're like a paradox. You're skills are both limitless and not "limit"- less

[@blackpenredpen]

hahaha thanks

[@gvacv]

3:16:10 still watching, indeed!!! I really really appreciate your effort, professor! It's a little bit sad when you say your arm hurt or that you're sweating, but then it gives me strength to not give up too!

[@blackpenredpen]

Thanks! I run marathons, so I am determined in the things I do. I am happy that this video motivated you as well!!

[@Lil_electrician]

I watched the 100 integrals and also the 100 series, they are very helpful for getting the main idea and getting practice for them thank you

[@blackpenredpen]

Great to hear! Thanks.

[@mathesaurus3621]

These videos are genuinely helpful and great for people who are doing calculus 1 and 2, thank you for making these videos and making our lives much simpler

[@Johnny-tw5pr]

Q60: write x as e^lnx then you have e^(lnx+1/x) which from the previous limit we know tends to infinity so e^inf = inf

[@pawloszeyede5787]

Man is a legend! Thanks so much. I nailed my Calc Mid term because of your videos. God bless.

[@blackpenredpen]

Glad to hear! thank you. Good work on your end, too! : )

[@tim1753]

"doing limits is like a box of chocolate, you never know what you're gonna get" 4:19:56 Love this one

[@grindpalm]

"Limits are like a box of chocolates... you never know what you'll get" ❤

[@blackpenredpen]

hahaha!

[@saturn2334]

but you know its gonna be chocolate , if its a box of chocolate

[@trishaamps]

I'm in my 4th year of engineering and I needed a refresher on this. Thank you so much

[@pianodan1608]

It’s amazing that he is so determined to do math! Your dedication and perseverance inspire others!

[@najibqunoo7232]

the missing limit is 3 (2^x + 3^x)^(1/x) = ((3^x*(1+(2/3)^x))^(1/x) = (3^x)^(1/x) * (1+(2/3)^x)^(1/x) = 3(1+(2/3)^x)^(1/x) plugging infinity for x in this term we would notice that it would approach: 3((1+0)^0) = 3 we could also rewrite everything here in another form like: 2^x(1+(3/2)^x)^1/x if we got asked about the limit for x approaching negative infinity, we use the same procedure and notice 2((1+0)^0) = 2

[@najibqunoo7232]

it would be nice if you recovered this in a later video

[@blackpenredpen]

@@najibqunoo7232 Yea I plan to do so.

[@mistcipriano396]

Thank you, up

[@gruesomedevil5062]

i like how you dont solve questions for just the sake of it and actually teach everything i am doing this series as practice questions and learn a few things every now and then even though i have done this chapter 3 times from youtube

[@blackpenredpen]

Glad to hear. Thank you!

[@gruesomedevil5062]

@@blackpenredpen 🖤❤

[@johndouglasclark1309]

Still watching, Q48, you truly are so motivating, your dedication is motivating and makes me not want to stop working hard!💪

[@blackpenredpen]

Glad to hear!!! Keep up ur good work too!

[@505steel]

I just made it through Advanced Calculus/Real Analysis this summer because of this channel! Thank you!

[@blackpenredpen]

Great to hear!

[@farouk6437]

I didn't study the last two weeks for personal reasons, then the last day i spent the 7h30 hours on this video (with pause for doing exercises after he show the answer is gonna be a solid 15h). While chewing a watermelon chewin gum. The day of the exam i chewed the same watermelon chewin gum and i was able to recall the exercises from this video and the answers and explanation! I got a solid 94% final exam. Hope this advice can help some of you guys!

[@killer-bee0]

OMG that's really insane that you complete like 10 videos of 100 math problems🥶

[@God-ld6ll]

"your limits dont even exist"

[@rayanselmani480]

What do you mean about that

[@Mozalthiric]

@@rayanselmani480 has to do with limits and calculus

[@rayanselmani480]

@@Mozalthiric ⁦^_^⁩

[@AbhishekMishra-lt2fi]

sir you explain better than my class 11th science maths teacher she just a noob maths and God knows how she became teacher.

[@gustavosouza5600]

i am just impressed that someone could spend 7h just doing limits. i'll definitly watch it fully.

[@blackpenredpen]

Thanks!

[@gustavosouza5600]

@@blackpenredpen i'm really thankfull for your content, really. I'm from Brazil and here this kind of content is not commun and eazy to found in that level os quality. you're just amazing!

[@cymbalization9443]

Watched your video since the start of my A-level course last year, from not having a clue, to knowing more and understanding more in the different perspective. Love your vids, it’s really helpful in giving me ideas to solve my math problems creatively.

[@thygovanengeland8758]

His enthusiasm makes me want to do all his 100 series (which I am). Thank you for your dedication!

[@adamlopez2339]

I've seen the whole video, absolutely amazing. Appreciate the effort on your videos, keep going

[@blackpenredpen]

Thanks a ton!

[@elhaunterelegante545]

For those wondering about the limit of Q42, it is 3. I recommend to make it similar to an 1^infinite indetermination

[@mistcipriano396]

can you explain? idk how to make this without lhopital or special limits. I know it's 3 because i saw on geogebra but idk why

[@ScampSkin]

This is one of my favourite series on YT. I hope you will be doing more episodes although this is exhausting and time-consuming. You are really helping people and not only those who are students but those who try to self-educate and change their lives. Much respect my man

[@user-tt2po5wg7n]

He is a math menace! Someone give this man a raise!. this calculus master ain't got no limits .

[@ESOMNOFUONLINEMATH]

My role model. I do maths here, but I always salute you

[@armilo5]

Thank you so much for making these types of videos! The 100 integrals and 100 series videos were super helpful when preparing for my Calc exam ❤️

[@blackpenredpen]

Glad it was helpful!

[@StaticBlaster]

in ONE TAKE! holy jesus. This guy's channel should be called TheMathBeast, TheMathGod, or TheMathMaster

[@AeroStuffFPV]

Imagine forgetting to press record

[@pro.x441]

😂

[@redweg47]

04:54:54 the limit when then equation goes to infinity is 24/64=3/8. You are so awesome!

[@mustaphamomo9315]

a genius ,you need all the support.

[@Peter_1986]

Man, the epsilon-delta examples were explained a hell of a lot better in this video, compared to the chaotic mess from my math teacher.

[@bijanyeganeh8181]

I love your T-shirt and the fact that you are holding the mic for this long, love you man you are doing a great job, truly what a real teacher does

[@vickyvazzm3522]

I just want to thank you for your content, you literaly made me love calculus

[@blackpenredpen]

Happy to hear that!

[@YoavZilka]

Love these kind of videos. Can’t imagine how much effort you put in them

[@piashasan5136]

From Bangladesh 🇧🇩.... I am surprised what a patience in you... I watched fully.,🥰

[@sadnanjuhib]

Which grade are you in?

[@studiouskislay]

4:54:43 the answer is 3/8 5:16:36 the answer is 0 Thank you for everything sir ❤

[@kamoliddineshkobilov8926]

I got + inf for the second one

[@pooqy]

2:48:48 That should be x-1 in the square root ♥ If I spot any more mistakes I will be sure to add more as I watch all these 7 hours of footage

[@blackpenredpen]

Thank you!!

[@bhavyapal]

Glad you did this video about 100 limits it will help me in preparing for my upcoming exam.

[@Happy_Abe]

@7:00:45 the functions is sin(x) from 0 to pi

[@takeoverurmemes]

the captions may not be 100% accurate, but someone really went and put captions out for 7 and a half hours worth of video that's actually insane, bless whoever took the time to do that

[@tumelosibiya594]

Thank you so much, I am doing engineering and this calculus has been beating me up, writing an exam on Friday and I feel ready because of you. I've recommended you to many of my classmates since they were also struggling. Thank you.

[@Splixly]

you are the coolest guy i have ever seen on youtube

[@djezio258]

This is the video I was looking for! I might not watch it entirety by once, but fast-forward to the limits I have most doubts in solving them, then I'll come back everytime I need to refresh my mind about them. Math is power

[@konoveldorada5990]

Hey, I have a fun question for you :) In Ellipse, (x/a)^2 + (y/b) ^2 = 1. *Then find out (a/x) ^2 + (b/y)^2*

[@pratyushmishra4678]

If I am correct then it must be (2cosec2A) ^2 with A as the parameter with ref to auxiliary circle.

[@satestactmathtutor6570]

you are an absolute genius brother plz keep making videos for all of us.I am a machine learning engineer and your videos helped me so much through out my career

[@tim1753]

I finally finished this video, and I learned a lot. Thank you so much, you continue to make me love maths even more, as always

[@ayonbarua24]

I can't be more thankful to you Steve. So far you have been the carrier for me in my whole calculus study. I have learnt infinite amount of techniques through your 100 everything series and I hope that you will carry on this series. I hope to meet you once if I ever get a chance to do so. Love from Bangladesh.

[@user-pn6es6ju9v]

Man you're amazing, 😮 you stand 7hrs straight, holding mike and speaking for 7 hrs? I couldn't even able to finish watching your video

[@user-tp4mj8rl2f]

جزاك الله خيرا ❤

[@AltinoSantos]

Congratulations! Yes, you have no limits. You deserve 2 million subscribers! 👏👏👏

[@fernandocupil.6463]

Plsss dont quit making videos like this. You are my heroe. Eres mi ejemplo a seguir

[@Morphysince94]

the legendary series is BACK!!!! ❤❤❤

[@aysenuraydn9107]

i am from turkey, thank you so much this video. my english is bad but I understand you, thank you math language!!!!🤩

[@rshawty]

the title’s funny coz as a french person I read “100 limits” like “cent” (=“hundred” in french) + limits and it sounds exactly like “sans limite” which means “no limit”, lmao voilà jambon beurre baguette

[@DarkInTheNight]

Ham butter baguette?

[@rshawty]

@@DarkInTheNight yea

[@kangaiman5398]

This video makes my daily 2-hours-on-my-way-to-school so fruitful as a newbie to calculus. Thank you.

[@goodforyou9596]

The limit of his hard work is the limiting value of the logos on his t-shirt❤️

[@Joshinthetronk]

I have just started taking calculus and I absolutely find it fascinating!!!! Thank you for this wonderful video

[@theshadow9238]

As Calc BC approaches Semester 2, my homework approaches infinity

[@yohannesaschenaki5406]

Bro just calculus master...really you always inspire me to do more calculus love from 🇪🇹🇪🇹

[@mathsphilus]

Dude you went so far!! this is the true love of teaching, And also you r not boring I can watch this to the end. thank you so much.

[@jaykay2218]

Bro, you’re honestly an inspiration

[@blackpenredpen]

thanks!

[@Livio_05]

5:16:30 Well i guess you could say it's equal to (1-(1/x))^x.x, so a is -1 and b equals x. If you work this out with the formula, you'll get e^-x, but x goes to infinty, so you'll end up with 0

[@thex3001]

I watched all of it including 101 thank you so much you started from easy to hard especially thankful for the last part finally understood the connection between the Rieman sum, limit and Integral! and my analysis exam is next month!

[@DmitriNesterov]

Маньяк ты! Глубочайший респект ❤

[@CreativeDimension]

The answer to the question at 5:16:38 should be infinity as the expression will boil down to "lim x->infinity e^x", putting in the value results as infinity.

[@josepina9399]

For those wondering, the answer in the extra question at 4:54:50 is 3/8. I used L'Hospital's Rule 3 times

[@alessandrofaranca1309]

@@josepina9399 i don't think it is the answer, instead it might be 0 from 1/e^x

[@PetrilloProduction]

After first L'Hopital you get both x^8 so you can only watch about the coef. and get 3/8 :)

[@roshinis9986]

to use the L'Hospital's rule, you must first bring it to u/v form. I don't think you did that.

[@joshhh___]

@@josepina9399 After taking the natural log of both sides, you should get ln(L) = lim x->inf (x^2)ln(1-1/x). The right hand side can be written as ln(1-1/x)/(x^-2), which allows us to use L’Hopital’s Rule.

[@communist_amoeba3923]

WHAT! just multiply divide by (x-1) and we know x^n-a^n=na^n-1 obviously its 3/8

[@prapti2385]

My personal timestamps:- graphs:- Q)12 Q)13 Q)17 Q)28 Method of synthetic division 3:16:00 Sir I am still watching, thank you so much for making this video. I understand that it's really difficult to teach standing for 7hrs straight and that too to a camera. Hats off to you!❤️🤗

[@shivensaini3643]

Sir, I really thank you for The list you showed us at around 5:05:00. Very helpful, solving limits questions is very fast now.

[@blackpenredpen]

You are welcome

[@jeanalex7698]

Who made the subtitles is definitely a king

[@lostinthebluecity]

I did that ..!! I can't believe it myself.. I solved it from 1 to 100... thanks bro.. 🤘

[@VincentGoossens-tu8pd]

amazing teacher, lots of respect you make people enjoy math. incredible work thank you, you really helped me!

[@astrogds2816]

Thank you for these long videos, it really helps mastering the concept !

[@anayagrawal6550]

7:00:49 The function is sin(x)

[@icicle2180]

4:22:35 "Sometimes infinity can win too!"

[@DokterrDanger]

You can try 100 definite triple integrals next I believe you can do it

[@John010]

i know this might be rude, but this being the background "music" for doing homework is the best

[@Anonymous31416]

A Great thanks to you Sir 😊, to give us an ample amount of limit questions ( both graphically and algebraically)

[@edit3907]

We want 100 integration part 3 please ❤️☺️

[@joaovictorsouzadeandrade9713]

Now my Friday is gonna be interesting

[@andrewkachedwa3164]

You are much appreciated because u improved my performance in mathematics 🙏🙏

[@andrewstephengames1260]

I got 3/8 for 4:54:43 Edit: Also I got e^(-x) for 5:16:35

[@Happy_Abe]

@5:16:40 0

[@bsl3399]

It's a best way to learn mathematics, I wasted months to learn but only 6-7 hours is enough to solve math ,

[@warsw5262]

man's just math's own GOAT

[@amir_xtz922]

you are a life-saver❤. Watched this from Q1 to Q101 entirely.

[@mathsis9963]

i have my maths exam after 10 days ...watching this make me fire and now i am ready to burn out solving maths

[@QuranReact1]

For Q60, here is another way to do it : we can rewrite x*e^(1/x) as e^((x*ln(x)+1)/x). And previously in Q59 we already calculated lim as x goes to 0+ of ((x*ln(x)+1)/x), which is +infinity. So we can deduce that the limit as x goes to 0+ of x*e^(1/x) is equal to +infinity.