How to Find Any Limit: Part 2 (NancyPi)

Published on May 18, 2018 by

MIT grad shows how to find the limit at a finite value with a square root, (sin x)/x, or absolute value. To skip ahead: 5) for a SQUARE ROOT in the numerator or denominator (to RATIONALIZE by multiplying by the "CONJUGATE"), skip to time 1:14. 6) for a limit with something of the form (SIN X)/X, skip to time 5:38. 7) for an ABSOLUTE VALUE in the limit expression, skip to time 14:45. Nancy formerly of MathBFF explains the steps.

For PART 1 (How to Find Any Limit), jump to:
For LIMITS at INFINITY, jump to:

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5) For a SQUARE ROOT in the numerator or denominator: If you try plugging in the value for x and get a 0 in the denominator, and you cannot factor, get a common denominator, or expand to simplify the expression, then if there's a square root in the numerator or denominator, you can try MULTIPLYING by the CONJUGATE. For instance, if you have sqrt(x+1) - 3 in the numerator, you would multiply both the numerator and denominator by sqrt(x+1) + 3 because the "conjugate" just means a two-term expression with the sign flipped in front of the second term. This is a trick or technique that helps simplify because when you multiply out, or FOIL, the numerator you will get terms that cancel. It is best to leave the denominator factored, rather than multiplying out the terms since a factor is likely to cancel. Once you simplify by multiplying on top, combining like terms, and canceling any factors from the top and bottom, try plugging in the value again for x to get an actual limit value.

6) For the form (SIN X)/X in a limit expression: If you try plugging in the value that x is approaches, and you get 0 in the denominator, if your limit expression is something of the form (sin x) over x, there is a trig property that you can use to simplify. The property is that the limit of (sin x)/x, as x approaches 0, is equal to 1. If your expression isn't exactly (sin x)/x but instead has something like 2x or 3x inside the sin function, like sin(2x) over (4x), you can use the same property but first have to rearrange the expression in a way that matches what you need, as shown in the video. NOTE: Be careful not to confuse this trig property with another, very similar, (sin x)/x expression for when x is approaching infinity. That property states that the limit of (sin x)/x, as x approaches infinity, is equal to 0. Check out the video on limits at infinity for an explanation of how to use that expression.

7) For an ABSOLUTE VALUE in your limit expression: If you try plugging in the value for x and get 0 in the denominator, and you have an absolute value in your limit expression, you will probably need to re-write the limit expression using the piecewise definition of the absolute value function. You will then have an expression for the left-side limit and one for the right-side limit. If you evaluate the left side and right side, and the numbers agree, then that is your limit value. If the two sides do not have limit values that agree, then the limit does not exist.

For more of my math videos, check out:

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  • PullOutGameWeak 4 years ago


  • J Torres 4 years ago

    Just in time to prep for my Calc final! Thanks for the educational vids 🙂

  • amty 4 years ago


  • Antonio Mayoral 4 years ago

    wooohooo! Yayayayayay! Thank you!!

  • Daniel Thompson 4 years ago

    Nancy’s on fire 👍 the best ever

  • Shoaib Amjad 4 years ago

    GooD work.

  • Upfrontgameplay 4 years ago

    Thanks again Nancy, I’m a limit ninja now due to your help! You’re the best!

  • Andrew Fitch 4 years ago

    Does anyone else watch these because of her amazing voice? She’s like the Bob Ross of math

    • Jeremiah Carr 3 years ago

      I watch her for scientific purposes 😉

    • Jeremiah Carr 3 years ago

      Just kidding thats gross and not cool

    • Lastrevio 3 years ago

      morgan freeman

    • Martin basha 3 years ago

      I don’t take any math classes but I just watch her videos because she’s cute 😂😂

    • matar mbe 2 years ago

      … and her smile

  • Cody Stewart 4 years ago

    Yayyy!!!!! I’m so glad you’re here!!!!

  • uzair mirza 4 years ago

    Why am i paying international tuition when this is free but both of the contents are the same?!

    • KHC Online Education 4 years ago

      uzair mirza revolution is coming

    • Star dust 4 years ago

      I am paying international tution too !!! 😡

    • 1LIFEtoWIN 2 years ago

      Same reason why anybody pays for any kind of education so you get that certified price of paper for virtue signaling on job applications otherwise they don’t care if you were self-taught through other means unless you somehow obtain work experience from being an entrepreneur at which point, why work for anybody else when you can be your own boss. Harvard is now offering free online classes too but you have to pay to get the “credits” for the class.

  • Maurice Upton 4 years ago

    Could you do some on where all these formula is used and how its applied in life. NZ.

  • Carl Johnson 4 years ago

    Can you go over some advanced topics? Like some hardcore proofs involving groups and symmetries or vector calculus?

    • Suki Suuuki 4 years ago

      Carl Johnson yesss or how to graph

  • Sam Heinrich 4 years ago

    *Love the videos! DON’T GIVE UP NANCY*

  • Nikul Bhati 4 years ago

    Hi Nancy u are beautiful and thanks for calculus and plz cover all topics of limit step by step…

  • KHC Online Education 4 years ago

    Glad to see u back

  • KHC Online Education 4 years ago

    Good work is always appreciated

  • KHC Online Education 4 years ago

    And it should always be promoted

  • Suki Suuuki 4 years ago

    thank u♡

  • Suki Suuuki 4 years ago

    graphd are much needed (like if u agree) plz do a video about them u know those graphs that u use limits to find where they are that looks like snakes 📈📉i still have trouble with them..♡♡♡♡

  • uzair mirza 4 years ago

    Please cover lim at infinity & lim at infinity for integration.

  • Elsif 4 years ago

    These videos are just so relaxing. I watch even when I know the content 🙂

    • Ubi Bhatt 4 years ago

      I know what is so relaxing 🙂

  • Steven Zoldos 4 years ago

    Hi Nancy, great videos! For the absolute value example, why do you show that x =2? Since you can never divide by zero, the domain of this rational function should “exclude” x=2, correct? However, in your example, the piecewise graph shows a “solid dot” at the point x=2. I think it should be an “open circle” from both the left and right limits. Likewise, the piecewise function should not contain x=2, agree?

  • Nazar M 4 years ago

    Quick suggestion, it’s great to see your face, however at times it can be hard to read the writing due to low contrast between the background and the text color.

  • robwin007 4 years ago

    Nancy, I am so thrilled you are back. You were missed immensely.

  • robwin007 4 years ago

    Nancy, Do you have a video where you find the area under the graph along with slopes – I guess I am asking for calculus examples?

  • Michael Geinopolos 4 years ago

    Instead of multiplying by the conjugate, why didn’t you just do L’hopitals rule?

    • Mil Zex 4 years ago

      I would hav asked the same question if she used l’hopital’s rule 😁

  • Jubair Pial 4 years ago

    hi. can you make a video on laplace transformation

  • Ahsanul Houqe 4 years ago

    It was awesome tnx…Nancy

  • Omar El Sayed 4 years ago


  • Omar El Sayed 4 years ago

    What about bounded integrations !

  • Omar El Sayed 4 years ago

    Area and volume of bounded integrations

  • Raghupathi K 4 years ago

    Respected madam.
    could you please tell,
    in engineering field where we really apply math concepts ?
    please tell life time examples

    • Maat Jazmim Luiz Nelson 4 years ago

      Raghupathi K 😂😂😂😂

  • Rohit Mistry 4 years ago

    this was really helpful thanks sm! Can you do a video on integral applications? Like finding volume by rotating around an axis, area between curves, and using cross sections? Thanks so much for your help

  • Conor McCracken 4 years ago

    lmao she has a weird knack of uploading these videos at the most convenient times

  • Jozef Aerts Wiskunde 4 years ago

    Why is lim x–> 0 sin 2x/2x = 1 ? It has to be lim 2x-> 0 sin 2x/2x = 1

    • Mil Zex 4 years ago

      Because on X–>0 ,x can be any parameter like (2x) or (t) or (3t)

  • OrphanPaper 4 years ago

    love your video ,well done ,

  • keshav kapoor 4 years ago

    Hey nancy please teach us some applied mathematics for physics. BTW nice work👍👍

  • Scarlett Martins 4 years ago

    Hey Nancy, can you post your videos of logarithms? They were amazing and I really need them for my maths class. Thank you for all the videos, they have been so helpful.

  • RubiMercuri 4 years ago

    Hi Nancy i just found your channel and im loving how well you explain things. Please dont stop uploading. Especially calculus videos. You make math easy to understand! I start calculus for the first time in the fall and will study it till then 🙂

  • Ian Carlos Santos 4 years ago

    Nancy, you are my crush!

  • Leonardo Camargo 4 years ago

    Imagine a NancyPi ASMR version…

  • Aasutosh Acharya 4 years ago

    she looks like someone that would be in a shampoo commercial.. XD

    • StarDagger Rihannsu 4 years ago

      I just need to find 4 or 5 women like this, smart and hot!

    • Chukwudi Obi 3 years ago

      True that

  • Ronald Jensen 4 years ago

    Why not just invoke L’Hôpital’s Rule and skip all the algebra?

    • Paul 3 years ago

      Tallis Dawson i was taught derivatives before limits specifically so i could use L’H instead of all the pointless algebra

    • InStinct 3 years ago

      @Paul How are you taught derivatives before limits when the derivative IS a limit? That makes no sense at all, you literally just memorize a bunch of formula and rules of derivation then, and don’t really understand a thing about it.

    • Paul 3 years ago

      InStinct because i went back after limits and covered the formal definition of a derivative. i have a masters in applied calculus so i don’t think i just memorise formulas…

    • InStinct 3 years ago

      @Paul Well yes, you went back, but I think for most people it would get damn confusing. At first you definitely just memorized formulas, because without being able to calculate a limit you can’t calculate a derivative. It just makes a lot more sense this way, and there is a reason why this is the way it’s being taught at almost every school and university that I know of.

    • Paul 3 years ago

      InStinct you’re saying i got taught that way, i didn’t. it’s simply just easier to do limits second

  • Neelpritam Lahon 4 years ago

    So good videos that there are no dislikes even after 2.1k views 😯😯😯

  • moosekabob2piplus1 4 years ago

    What equipment do you use?

  • Praveen Sreekuttan 4 years ago

    Nancy thankyouuuu very much for all the videos

  • Sukeshini Dupare 4 years ago

    Want some inverse trigonometry videos

  • Ziyad George 4 years ago


  • McKenzie Baird 4 years ago

    Your videos are so awesome and helpful! I would love if you could cover how to do approximate integration and the area of a surface of revolution since I am struggling with those concepts currently.

  • D W 4 years ago

    Math Megan Fox!

  • PhysicsHelps 4 years ago

    Like a… ninja… 🙂

  • Hussaan Alvi 4 years ago

    She is left handed ?

  • Eric Warda 4 years ago

    Just in time for my Calculus class and test on limits. Thanks so much Nancy!

  • Mobbsidian 4 years ago

    You know, if you joined and our STEM community there, you could make quite a bit of money from your videos – maybe itll inspire you to start it up again? A shame to see it stop!

    Feel free to msg me for more info at – i can help set you up and pretty much guarantee income and a great community of like-minds!

  • _____ 4 years ago

    I love how you organize everything into blocks like this. It can be overwhelming having the different techniques individually floating around my mind and you make it so much easier :’)

  • Marci Bebout 4 years ago

    Hello I was wondering if you would be working with differential equations I will be starting my class next month and learn more from youtube videos than class. Thank you!

  • Noor Habib 4 years ago

    Your so helpful, you have done a great job 😀

  • Decaf-Math ASMR 4 years ago

    Hey! Fun to find a fellow MIT grad here. Just started my channel. Are you still making math videos? This whiteboard and fast forward effects are cool. Keep up the good work =)

  • Oh Jetty 4 years ago

    Nancy is so hott.

  • Guty666 4 years ago

    u should do asmr videos

  • Justin Santos 4 years ago

    Can you also discuss double angle, half angle, triple angle, product to sum and sum to product formulas? Those are the formulas I have trouble memorizing myself.

  • Ahmed Habib 4 years ago


  • wiloux 4 years ago

    why can you simplify (x-8)/(x-8) in the limit if x goes to 8? that’s like simplifying a « 0/0 » situation

  • José Ignacio Naranjo 4 years ago

    I love you so much………..I am one of the millions who love you so much……….thanks a lot for your great videos…..God bless you forever.

  • Mazhar Abbas Bukhari 4 years ago

    nice work,Miss nancy plz make a video lesson on probability ,factorial and statistics….

  • Jerry Gundecker 4 years ago

    I figured out how you write like that. You are 100% dyslexic, right?

  • Juniermie Pagdato Inopiquez 4 years ago

    Thanks a lot NancyPi <3

  • Dawit Wolde 4 years ago


  • Abdullah sheikh 4 years ago

    What if we get infinty on both left and right limits ?

  • Qermaq 4 years ago

    I drank every time you said “OK”. Yipes!

  • Nneka W 4 years ago

    you are a godsend

    • Usama rafieck 2 years ago


  • Hatem Ibraheem 4 years ago

    Big love Here from Egypt for your ( EFFORTS ) I really respect you Nancy :))

  • DancingwiththeDocs 4 years ago

    This helped a bunch! Thank you!

  • mrJwlock 4 years ago

    Thank you Nancy, the best!!

  • Samuel Williams 4 years ago

    I owe you big time! I’ve gone back to school to finish my math major and go to dental school and I’m having to relearn all of my calculus (its been 8 years since I first took Calculus 1!). You are helping me so much! I work two jobs full time around school and never get a chance to go see my professors during office hours, but thankfully youtube is never closed! Thank you for your awesome contribution to the learning community =)

  • Amanda Brito 4 years ago

    love you <3

  • Suresh Darsi 4 years ago

    Please do lectures on probability ans statistics

  • Ross Warber 4 years ago

    Here to become a limit ninja!! Thanks yet again, Nancy!

  • JC Avenilla 4 years ago

    You’re a better teacher compared to my college professor 😭😍

    • Random Autonomous Drone Pilot 3 years ago

      Third world schools unfortunately are not as good as American schools. No matter what anyone says. Wonder why some people think they’re so easy even though the US always has good tech that works. Someone is lying lol.

    • Chukwudi Obi 3 years ago

      College professors are souls from hell

  • khaled qaraman 4 years ago

    Hi Nancy … At 21:33 you have a little mistake since the function is not defined at x=2 so the point (2,1) must be white too just like (2,-1) does not belong to this graph

    • Michael Ayeni 3 years ago

      yes at 2 a vertical asymptote is reached

  • Michael Balbuena 4 years ago

    She’s absolutely beautiful

  • Brett Carter 4 years ago

    “You’re going to be like a ninja….. but for finding limits at a finite value…”

    • rayagainstthemachine 4 years ago

      LOLLLL I was gonna post this exact same thing and I can’t believe it took so long til 2 days ago for someone to say it

    • Lieh Honoridez 4 years ago

      And she was like stifling her laugh

  • Cassidy gaming and more 4 years ago

    Nancy can you please explain how did you got 3(square root x+1+3) twice?

  • Cassidy gaming and more 4 years ago

    How did you came by 1/6

  • Brownish Sage 4 years ago

    I’m amazed by her ability to write backwards

  • Nmz 4 years ago

    Really a big help 😊

  • xx SHASHA xx 4 years ago

    you’re awesome !!

  • Victor Mejia 4 years ago

    Wow I love your videos I wish you the best!! Your videos are so understandable and helpful!!!

  • Naweed Babakarkhail 4 years ago

    what about u-substitution or the long division factoring?

  • David Granados 4 years ago

    Some log/exp limits examples would be great, we’re having issues at calculus with those ones.

  • Ferrulle 4 years ago


    • AJEÚ GÓMEZ TOC 3 years ago


  • Sonu s 4 years ago


  • Barnaby Drew 4 years ago

    Do you never use L’Hopitals rule? Is it better not to use this?

  • Anj Sereneo 4 years ago


  • irakoze Arnaud gael 4 years ago

    can you make for me (x-8) to be the conjugate cause I did it and I found 3/16 is it answer

  • Tarik Hacialiogullari 4 years ago

    Helal abla, thank you very much!

  • Lamin Colley 4 years ago

    you are blessed…keep up the good job

  • saransh kumar 4 years ago

    hello mam do u hav any videos over fourier transform

  • flimbosquest 4 years ago

    Finding limits and writing beautiful, readable text backwards on a transparent board have been on my skills-that-are-impossible-to-master-list for a long time. Now, of the two, only the writing-backwards-part remains on that list (together with writing readable handwriting in general). Thank you for an excellent explanation and presentation of the subject!

    • James Allbee 4 years ago

      She doesn’t write backward, the video is mirrored in editing. Her explanations truly are amazing, though!

    • flimbosquest 4 years ago

      @James Allbee Aha, that makes sense, silly me :-). Thanks for clearing that out. It’s still a very interesting and entertaining way of presenting her explanations, like you say. I never believed that David Copperfield could really fly, though. Promise 🙂

  • Victoria Mcgarrett 4 years ago

    How is lim4xsin5x/sin4x * 5x/x = 5
    Lim 4xsim5x/sin4x is 1 i get that but 5x/x isn’t it 0 ?

    • Miguel Bernal 3 years ago

      the X’s cancel out

  • Karim Gubashi 4 years ago

    Thank you mis Nanci

  • Rohama Abundo 4 years ago

    I wonder how you write that way

  • mangesh KENDRE 4 years ago

    Nice video

  • Iris Onicar 4 years ago

    Thank you so much😭💕 please keep uploading lessons

  • SPIKE 4 years ago

    At 3:56 Well you could have made the example shorter by just using a2 – b2 formula! 😀 btw you are teaching amazingly n tbh u r the best! 😊

  • Samuel Lechisa 4 years ago

    god bless you…

  • Gopalan PN 4 years ago


  • Hannah Clark 4 years ago

    this is helping SO MUCH!! Ap calc test tomorrow

  • dik2bik 4 years ago


  • Habib Alwy 4 years ago

    Does anyone realised.. That.. She.. Wrote.. In.. The.. BACKWARD DIRECTION?? Or its just my eyes being wrong

  • StarDagger Rihannsu 4 years ago

    You should be showered with gifts, and men and women to give you pleasure!

  • Alwyn Nicholas 4 years ago

    Great work Nancy!. I am trying to get a simplest way to express a calculated limit. Would I be correct to say that the limit (as calculated) is the value at which the X value cannot be? In other words, if the X reaches that value then the two points on the secant would meet at the same point (tangent) and therefore there would be a zero in the denominator, rendering in indeterminate or undefined?

  • Kemal Göçer 4 years ago

    I’m Turkısh but I wanna prefer listen and learn maths in English. Especially this channel also her voice perfect

  • Joshua Tovar 4 years ago

    Math question for you guys: does anybody know the limit to Nancy’s beauty?

  • rus pasawa 4 years ago

    Ur so cute when u catch ur breath😂😅

  • مفتاح مطول 4 years ago

    Thanks Nancy

  • Elisabeth Skorski 4 years ago

    You are saving my life in calculus right now!

  • Renan Hiramatsu 4 years ago

    At 13:50 confused me a bit but I think you only made a written mistake where you put 5x in the bottom(making it be 5x^2), being only 5. Am I right? (When u multiplied top/bottom by 5x)

  • Elton Lucien 4 years ago

    I understand…WTF?

  • Paloma Colunga 4 years ago

    youre the only channel i come to for help with math. you have all the material covered, and explain it so thoroughly. thank you!!!

  • Kailik Faulk 4 years ago

    Ninja analogy was horrible, stick to math lol.

  • Apple baba 4 years ago

    doyou have tangent?

  • Swaroop Rajpurohit 4 years ago

    Why didn’t she tell the L’Hospitals method?

  • Anthony Maestas 4 years ago

    Ok so I think I got it, she is writing on a mirror. Damn that took a lot of thinking, now back to math.

  • sivan ferna 4 years ago

    For 11:20 can’t you just multiply the top by 2 to get 4x and then multiply both by 1/2. I did and I got the same answer just like the previous question

  • Randall Blake 4 years ago

    Please do a video on epsilon-delta proofs.

  • hahahahahhaa Haokip 4 years ago

    Best of the best

  • Wilmarc4 ! 4 years ago

    You are awesome!!!!!! I learned more with you than my professor about limits. Good Job Nancy

  • أحمد بحسيس BAHSIS AHMED 4 years ago


  • Alana Star 4 years ago

    BTW, Nancy please keep using algebraic methods because the L’hospital rule or whatever is not accepted by ever professor, at least at the start of the semester. Technique matters.

  • Sajit magar 4 years ago

    hey lefty let me remind you im  also lefty 🙂

  • Alimul Raji 4 years ago

    l really like your vedio..that can help me much in calculas

  • Madeline Abigail 4 years ago

    Sooo… Practically, in absolute values, usually limits do not exist??? Not all the time but usually

  • Ryan Ahmed 4 years ago

    13:38 is the worst explanation ever
    please redo it

  • Robert Vaca 4 years ago

    Pretty and beautiful almost as much as the number of digits of Pi. I’ve fallen in love with you as fast as Light loves to run through the Universe.

  • Amirah Hidayah 4 years ago


  • lethukuthula The Libra 4 years ago

    this lady is brialliant

  • Siddhant K 4 years ago

    make video on exponential and logarithmic function

  • Harold Chisunzi 3 years ago

    making my life of maths simple

  • Sdw-OrbZ- 3 years ago

    can you help me find the limit as x approaches zero for sin 2x over 5x. I tried the rule that you are using in this video, however, the workbook that I am using has answer key and it tries to explain that i should take the derivatives of both numerator and denominator then substitute x=0. Any help would be greatly appreciated.

  • Matthew Berrios 3 years ago

    I want to say thank you for these videos on limits. It greatly helped me understand how they work and made the final exam an absolute breeze! Your videos are very understandable.

  • Penguin Bros 3 years ago

    By the power vested in me, I invoke L’Hôpital’s Rule to expedite the problem!

  • James Arnes 3 years ago

    22:16 LOL Yeah right! Limits are my favorite. I like them almost as much as going to the all night dentist. They’re especially fun when absolute values are involved. I look forward to them almost as much as a trip to the laundromat. Thanks so much for going over them step by step so they made more sense. A few more examples and I’ll be able to teach this class.

  • Suresh Chaudhary 3 years ago

    How to find you in my life forever Nancy, what can I do, answer please

    • timcritt 3 years ago

      Yeah, she’s definitely going to answer this message. It’s not creepy in the slightest. lol.


    Very nice. Thank you!

  • Amir Forgotten 3 years ago

    Actually use HOP is very more useful…
    U can use it also

    • Red Angry Bird 3 years ago

      It might be more useful but more complicated.

  • TechBro 3 years ago

    She has Gray Eyes <3

  • Chris Davison 3 years ago

    Wow, Nancy, your smoking today, I must say. Whatever you’ve done, keep doing it. 😉

  • Micheal Errins 3 years ago

    who else thinks she cute and smart perfect combo!!!!!!!!

  • Brett L 3 years ago

    I just melt when she explains something i dont understand.

  • Caleb Donaldson 3 years ago

    Thanks for the help on that! I’m in Honors Pre-Calc and was finding these complex forms of limits somewhat confusing.

  • Dyami Anguiano 3 years ago

    For absolute value problems, what would happen if absolute was in the denominator?

  • AnselAlly 3 years ago

    What happens if the Numerator and the denominator both have absolute value?

  • Nate Private 3 years ago

    So smart and so beautiful!

  • Red Angry Bird 3 years ago

    I genuinely came here to learn limits,
    and now I feel like a ninja !! 😋

  • Shivansh Singh 3 years ago

    Lim sinkx/x=k
    E.G sin5x/x=5

  • Thomas K 3 years ago

    So when finding the limit using the absolute value, you got -(x-2)/-(x-2) = -1

    Shouldn’t that answer be equal to positive one!

    After all, it’s a -1/-1 ; A negative being divided by another negative….

    Thanks Ms. Pi,
    You’re beautiful!

  • Sara Toborowski 3 years ago

    Nancy has a talent of making things simple to understand and remember! thank you!

  • Mark Brown 3 years ago

    Beauty and Brains!!! She is not only helping me with math but i think I’m in love!! Lol!

  • Carlos Gonzalez 3 years ago

    This channel deserves way more subscribers.

  • Aaron Jackson 3 years ago

    Yo how the heck do you write so fast?

  • Michael Prozonic 3 years ago

    at 4:00 you FIOLed instead of FOILed lol

  • Ariana Picazo 3 years ago

    I correctly completed my first limit. Thank you! You’re a blessing

  • Paulo R Menezes 3 years ago

    She is prettiest than Megan Fox and has amazing math skills.

  • Homayoun Yaqobi 3 years ago

    Great work nice lecture

  • Ajay Joshi 3 years ago

    doesn’t l hospital rule comes along with the topic of limits

  • nmhicks 3 years ago

    Thanks for the great video. This really helped me. 🙂

  • Reem AlShanbari 3 years ago

    Awesome explanation!

  • محمد فيصل 3 years ago

    Thank you , really you make this object very easy

  • samia sama 3 years ago

    u cleared all my doubts.thanks. are u a professor?

  • johnnynyc00 3 years ago

    What if the absolute value is in the denominator?

  • Chance Seliskar 3 years ago

    I used to listen to lofi while studying. Now I listen to Nancy.

  • Lil Ugly Dude 3 years ago

    what about continuity

  • jai ellie Hawihao 3 years ago

    I really love your videos nancy it really help me a lot on my calculus subject.
    And anyways i love your voice and your so charming .

  • srinivasa rao 3 years ago

    I need finding limits including sgn function and Greatest integer function, Indetermine forms for my JEE Exam… The ones you discussed are basics….
    But thanks 🙏

  • Jennifer Juarez 3 years ago

    😭 Thank u!

  • ashish pandey 3 years ago

    I came at the video bcoz of your beauty and i watched it bcoz of your genuinity and credibililty

  • Moroccans in Russia 3 years ago

    How to write on that wall ….?????

  • Small H 3 years ago

    Your videos are very satisfying 😁 thank you

  • SARANG ABBASI 3 years ago

    please use dark marker.
    okay its visible but i mean dark marker would be perfect.😉

  • IITian Reacts 3 years ago

    hey its Satyajit from IIT , India …..would you like to make a video on limit for multi variable function?

  • Rena Nario 3 years ago

    hi, I was abit confused about the first equation, your numerator is (x-1)-9, isn’t that -9x+1? but why did it became x-8?

    • Jordan 3 years ago

      That tripped me up as well but it’s all about the parenthesis. (x+1)-9 = x-8. However, (x+1)(-9) = -9x-9.

    • Rena Nario 3 years ago

      I meant -9x-9😅😅

  • LISSA MERO-LOPEZ 3 years ago

    what happpens to the 9 in -9x-8 for 5:00

  • incredible TAWANG 3 years ago

    I have some troubles with absolute type of limits😩😩

  • Ballard Mayes 3 years ago

    Currently using these as a refresher for my Cal A midterm. Thank you a lot!

  • tlamelo sebopelo 3 years ago

    you are beyond my teacher even.i understand more when its you teaching.

  • Lucius Irving 3 years ago

    Thanks! I’m gonna need this for business.

  • Jacob Lane 3 years ago

    Adjust playback speed to x1.25 and thanks me later

  • Iron Langkoi 3 years ago

    Learning ang hardening at the same time!!!😉

  • Iron Langkoi 3 years ago

    Oohh Nancy you can turn me on!

  • Marius van Gent 3 years ago

    I am missing the limits on which you have to use Taylor expansion :/

  • Noor ul islam 3 years ago

    loved it like every single one other…

  • Jeremiah Carr 3 years ago

    God she is something else I often forget I’m watching a math video

  • Maths AND Physics Made Easy 3 years ago

    How do you fast forward

  • Evaristo Lilungwe 3 years ago

    wow this is amazing, my lecturer only covered 3 topics out of 7 topics in calculus. so these videos really make things so simple. i rate them 5 stars (*****) thank you so much

  • Ellen 3 years ago

    omg nancy your jokes are mainly what keeps me going lol

  • isobar 3 years ago

    A beautiful lady…teaching a beautiful subject. Just one query…at 14.06 shouldn’t the limit be indeterminate since lim as x approaches 0 of 5x/x = 0/0? Were you just trying to catch us out…or am I incorrect?

  • mata2nz 3 years ago


  • Matematicas 3 years ago

    i like your videos but you dont upload much

  • Henry Trujillo 3 years ago

    I fall asleep with her videos

  • Rishi Lodha 3 years ago

    If all the teachers in school are like u students never bunk the class

  • obaidh Syr 3 years ago

    Thank you so much helped alot✨

  • WheresTeddyNow 3 years ago

    Please please please… stop saying “cancel out”. A puppy dies every time you do so. 🙁

    Hyperbole,? Yes. But an important distinction in Maths; things subtract or divide out. They DO NOT ever cancel out.

  • Rajendra Khedekar 3 years ago

    Please solve some more examples

  • Brian Fisher 3 years ago

    Can I just thank you for taking the time to edit in the fast-forwards? I’m learning it either way, but it makes it even more classy. Stay classy, Nancy Pi.

  • John Vandersall 3 years ago

    i am sorry i watch these vids for youre beauty so hot

  • Pyro 3 years ago

    My limit is 8 pints.

  • Mahe mamu 3 years ago

    how to find two limits in one function!

  • Brian 3 years ago

    At 0/0, l’hopital rule is easier!

  • Mustafa Noor 3 years ago

    Nancy we need laplace transformation

  • Shoaib Ahmed 3 years ago


  • Abhin Francis 3 years ago

    Thank you

  • Utkarsh I. 3 years ago

    oh wait, she’s a lefty

  • IMBIue 3 years ago

    This is the same video as part 1

  • Sheryl 3 years ago

    Thank you so much for your videos! Really great help for me in surviving Calculus 🙂

  • 이성훈 3 years ago

    You are a Bob Ross of math

  • tsvetomir 530 3 years ago

    Where did -9 go after rushilizing

  • Eris Socratou 3 years ago

    I think there’s a method that’s still missing.
    Fractions of two high grade polinomials
    I mean:
    lim x→-1 : (3x^3+8x^2+7x+2)/(2x^3+7x^2+8x+3)

  • Al sami 3 years ago

    Hey gays😂😘 schön

  • JACOB HARMON 3 years ago

    Saved again by Nancy talking about math with ACTUAL WORDS!!!!!

  • Phantom_Oz 3 years ago

    You’re smart and beautiful.
    Loved the video, thanks

  • Joseph Siciliano 3 years ago

    is the most confusing part for me.

  • Jordan Hill 3 years ago

    learned more watching this video than a semester and a half of university THAT I AM PAYING FOR! thanks so much

  • Dicho Dichov 3 years ago

    marry me pls

  • Umer Amer 3 years ago

    Such a clean explantation, am your fan

  • Mathematics Lover 3 years ago

    Had anyone noticed that when Nancy was writing very fast, a slow sound was produced??

  • james geda 3 years ago

    I don’t agree with you about absolute limit
    Bcoz if x is left approach to 2 but not equal 2 so ,x-2 =-ve,so the numerator and denominator -ve and the results is +1 also in second case please if not I need explanation from you

  • Mathematics Grade 12L 2 years ago

    Good Teacher ❤

  • Alexander Bacharyshvili 2 years ago

    How did you get the right limit equals to 1 in the last problem¿ shouldn’t it be 0/0 as x approach at x-2/x-2¿¿¿

  • Anastasia Zharkova 2 years ago

    Just wanted to say thank you thank you thank you

  • FromFilmToCode 2 years ago

    Little dry jokes.

  • FromFilmToCode 2 years ago

    but the Θ = 2x
    and bellow lim we have Θ = x -> 0
    x = 2x ??

  • OMKAR BABAR 2 years ago

    Miss. Megan Fox of maths.

  • S H 2 years ago

    There’s no limit. I want to find you and marry you. XD

  • Karen C 2 years ago

    Why has nobody mentioned the fact that she’s been writing backwards? (That’s crazy)

  • Soumyajit Bose 2 years ago

    Thank you maam.. Love and respect from India.

  • shaima balakrishna 2 years ago

    wish u wer my tr in my school days.

  • BATTL EX 2 years ago

    Love your videos

  • matar mbe 2 years ago

    Nancy I love you. I’d just like to tell you what I feel in front of those witnesses that wouldn’t expect to hear what I mean.

  • Rahul Chaurasiya 2 years ago

    Love from India

  • Rainsong 777 2 years ago

    02:12 Trick :
    Multiplying with the conjugate…
    2-term x by the same, only the sign in the middle changes

  • Fredy M Guevara 2 years ago

    Thank you so very much for all your help!

  • Kotha Lakshmi Kusuma 2 years ago


  • 2D Senpai 2 years ago

    Nancy, how are you memorizing the trigonometric rules + algebra rules…this is calculus 😭

  • Carlos Dominguez 2 years ago

    She explains very well, but for some reason I can’t concentrate

  • Reghan Funderburk 2 years ago

    Wait, is she writing everything backwards?

Comments are closed.