How to Find Any Limit (NancyPi)

Published on May 15, 2018 by

MIT grad shows how to find any limit as x approaches a finite value/constant value (and not infinity). To skip ahead: 1) For an example of PLUGGING IN/SUBSTITUTION, skip to time 1:45. 2) For FACTORING to simplify, skip to 3:53. 3) For GETTING A COMMON DENOMINATOR, skip to time 8:09. 4) For EXPANDING by opening up parentheses to simplify and find the limit, skip to 12:01. Nancy formerly of MathBFF explains the steps.

Jump to the PART 2 video ( for how to find the limit for: 5) a SQUARE ROOT in the numerator or denominator (to RATIONALIZE by multiplying by the "CONJUGATE"); 6) something of the form (SIN X)/X; or 7) an ABSOLUTE VALUE in the limit expression.

For LIMITS at INFINITY, jump to:

Follow me on Instagram!
Follow me on Twitter:

1) TRY PLUGGING IN/SUBSTITUTION: The first way to try to find the limit value is to plug in for x. In the limit expression, x is approaching a certain number. If you plug in this number and get a value that is defined, then that is your limit. HOWEVER, if you get ZERO in the denominator when you plug in, then you have not found the limit yet and need to try something else to find the limit value.

2) TRY FACTORING: If you plugged in the value for x, and you got zero in the denominator (or the form 0 over 0), check whether you can factor and simplify to find the limit. If the limit expression is made up of a polynomial in a numerator and a polynomial in the denominator, then it is a very good idea to try factoring because a factor in the top may cancel with a factor in the bottom to give you a simpler expression. Then, plugging into this simpler expression may give you an actual limit value.

3) TRY GETTING A COMMON DENOMINATOR: If you plugged in the value for x, and you got zero in the denominator, and you cannot factor the expression, you have to try something else. If your limit expression has fractions within a fraction ("a complex rational expression"), try getting a common denominator in the expression. Use algebra to get a common denominator between the two fractions that are in the numerator (or denominator), and when simplifying, terms may cancel so that you have a simpler expression you can plug into to get a limit value.

4) TRY EXPANDING/OPENING UP PARENTHESES: Again, if you plugged in and got a zero in the denominator, and you can't factor or get a common denominator, consider opening up parentheses and expanding expressions by FOIL-ing or multiplying out and combining like terms. Simplifying in this way may lead to a simpler expression you can plug into to get a limit value.

For more of my math videos, check out:

Category Tag


Advertise here. Telegram, Signal - Call/message +1-868-308-4028.


  • Lycan_system 3 years ago

    Can u make a vid on absolute modulus functions and graphing them ??

  • Tashi Pearson 3 years ago

    how did she get 2/3?????????

  • Shaun T 3 years ago

    Thank you! This is excellent.

  • Mallika rai 3 years ago

    If we get 0 by 0 form we can differntiate term and substitute the value of x,we can get the correct answer plz try it

    • Mallika rai 3 years ago

      Plz try this method mam u can get the correct answr

  • Mallika rai 3 years ago

    Shortcut L HOSPITALS law.Bingo u can find any advance type of problems. Plz comment👍

  • N /A 3 years ago

    I like cutiepie more (marzia aka pewds wifey)

  • Bleedingreen 3 years ago

    I have weird questions like ( e^mx-e^nx)÷x . Do u have any tutorial for that?

  • AL 3 years ago


  • MarieJoe Pichardo 3 years ago

    THANK YOU!! You’ve gotten me through from trig to calculus<33

  • Meshach De Silva 3 years ago

    I wish I had a math teacher like Nancy

  • Asmae Sabri 3 years ago

    Thank you From Morocco ❤

  • 凝视 3 years ago

    First time realizing math could be joyful, love u

  • saif shaikh 2 years ago

    Thanks Nancy 😍

  • Akshaymech Ahlawat 2 years ago

    nice l

  • Fried Milk 2 years ago

    Thank you NancyPi ..

  • andreathecat100 2 years ago

    4) you can factor as the numerator is a difference of two squares, namely (x+2)^2 and 2^2.

  • bhgtree 2 years ago

    Nancy’s beauty has no limit. 🙂

  • JP Nayak 2 years ago

    Father…. Mujhe isse padhna haiii

  • Tristan Hynes 2 years ago

    Yes miss.. I wasn’t paying attention .. got to distracted 🙂

  • thomas Mcdougald 2 years ago

    you saved my life.

  • Flywrite 2 years ago

    This video helped me out. Love how you present the problems and solve them!

  • Ali Aylan 2 years ago

    I’m kinda shocked by how easy questions that other people trying to solve. I’m from turkey and this kind of questions, you can’t see them in exams. They’re are asking way harder ones. I feel bad

  • Yuzhen Wang 2 years ago

    有没有什么网站,可以手写输入得到答案的錒。 any website. to get solution process of any limits calculation?

  • Afaq Khan 2 years ago

    Ur amazing I have learned alot from ur video can I get ur WhatsApp number

  • Basab 2 years ago

    If there is any math fashion model then it would be you mam

  • Brian Green 2 years ago

    So straightforward. Brilliant!

  • Le Alien 2 years ago

    What would i do without You Nancy….

  • Mathematics Lover 2 years ago

    Wow! Understood limits in class 8!!

  • S k nganga 2 years ago

    Nancy is a great teacher but this gets better when you learn l hopital’s rule

  • gabb 2 years ago

    Thank you so much! I’ve been struggling with solving limit problems but having these steps to go through is really helpful

  • Kshinobu 2 years ago

    I think calculus is driving me to insanity

  • Adil Masood 2 years ago

    helpful thanks

  • Arvin Monsod 2 years ago

    I love your videos Nancy very clear and simple. I wish my teacher’s do the same 😊❤💖😍

  • Mofazzal Student 2 years ago

    Thank mam

  • Yash Hooda 2 years ago

    Would totally replace you for my Ex 😩💦👌😍

  • Ajay R. Beniwal 2 years ago

    Nyc mammm….. fabulous look of u studies

  • Shojib Foysal 2 years ago

    in 12:46 time on your video, you said number 4 types cannot be done by factor but I did it by factor

  • Xavier Boipoi 2 years ago

    NancyPi madam, please bring the vedios for probablity and commbinations also , I like your vedios……

  • Augusto Pizzuti 2 years ago

    The square root of (1-5x) is defined for x <= 1/5, so 2 is not in its dominion nor in the border of it. The limit of a function is defined only for points where the function is defined, or for accumulation points of the dominion, or for isolated points of it. Thus taking the limit for x--> 2 has no sense by definition, which is different from saying that the limit doesn’t exist. Anyway, your videos are great, you’re extremely gifted as a teacher, and of course you’re helping a lot of people. 😊

  • ARJUN RAJPUT 2 years ago

    Damn she’s so hot that I can’t even look anywhere else leaving her cute face

  • 的话男孩 2 years ago

    foolish ASMR

  • hazim rasheed 2 years ago

    a big greeting from iraqi such a useful lessons

  • kalvin yu 2 years ago

    After flunking maths in high school I am trying to teach myself maths and I think I may have spent too little time on algebra. As now I’m struggling with these sort of issues with limits, I’m using the old soviet calculus text book, ‘differential and integral calculus’ by N. Piskunov. Does anybody know any resources I could use to get some more exposure to these algebraic problem solving techniques? Thank you.

  • Li Lu 2 years ago

    How is 2/3? but 3+1=4 and 3+3=9

    • Li Lu 2 years ago

      I mean 3+1=4and 3+3=6 so this should be 4/6 and not 2/3

  • زين العابدين محسن علي حسن 2 years ago


  • Steve Wolfe 2 years ago

    Pls Make some more videos of Limits these are School Level Questions
    We r Preparing for JEE and JEE don’t ask such easy Questions

  • Francisco André 2 years ago

    Great Video!

  • Veritas et Aequitas 2 years ago

    How do you find the limit as x >0 of
    [ Sin^7( π/6 + x/2) – 1/2^7 ]
    All over x?

  • Programming Interview Prep 2 years ago

    In the previous video, we were told the actual value of f(x) at a given x doesn’t matter, but just the value it approaches. Directly substituting x = 4 in f(x) would just give the value of f(x) at 4.

  • James Harwell 2 years ago

    You’re getting me through my Engineering degree… Thank you…

  • Oscar Gonzalez 2 years ago

    Great video. It was clear, concise, and straight to the point. However, did you change the initial math problems from the beginning? such as #3 and #4?

  • Dr. Digvijay Singh 2 years ago

    nice video….

  • Lily 2 years ago

    What I want to know is how she writes backwards

  • Martin Lenin 2 years ago

    I dont know what are you saying I see only your lips

  • MR 々͜͡AHMED 2 years ago

    اذا درسني رياضيات اله اصير خوارزمي العراق
    خرب حظي
    العراقي الي مر من هنا يجق لايك

  • Zeldwaugh 2 years ago

    LOVE these videos thank you so much. I’m confused about cancelling out the -x and x on step 3(common denominator). Is there a specific reason we can cancel those out? Thanks!

  • Zagros Atroushi 2 years ago

    The way she says `Denominator´ 😍

  • Bryson Batch 2 years ago

    your a amazing woman! you are great at explaining this. Thank you soooo much for making content on this.

  • Karen C 2 years ago

    Her voice is so soothing that in order to pay attention and not feel like I’m floating, I have to mute and read subtitles XD, will definitely subscribe if she does asmr

    • Beckett 2 years ago

      Same. Her voice makes me real sleepy

  • AldobernalTV Bernal 2 years ago

    7:34 isn’t the limit 3i?

  • ZapsterZatoo 2 years ago

    I am in love …

  • Y REMIX 2 years ago

    At the 4th part open up parentesis where did 4X came from and how

  • Giuliano Iantomasi 2 years ago

    happy belated anniversary babes.

  • S H 2 years ago

    Wifey, please button up the dress. Others are checking out those assets. 🙁

  • nagaad cabdi 2 years ago

    You are just solving not explaing where did you get

  • Sunil Agarwal 2 years ago

    Thnx for all

  • lidiya wolde 2 years ago

    6:48 who got it?😂

  • MathIsLife: Dr. Satbir Malhi 2 years ago

    Correction: Number/0 is not DNE, it is either +infty or -infty. DNE means when left limit is not equal to right limit.

  • BATTL EX 2 years ago

    You are great

  • ZHANG1973 Scorpion 2 years ago

    good teacher in mathmetics and good figure.

  • suhu wow 2 years ago

    wow,, my thinking is anywhere,, you are georgous and excellent,,,

  • Science is fun 2 years ago

    She is awesome and Thnks for everything Nancy 😍🔥

  • Mathematics Helpline 2 years ago

    excellent job

  • Lumai Mubanga 2 years ago

    u are amazing

  • Ivan Moloboco 2 years ago

    I love you

  • Ivan Moloboco 2 years ago

    I will not be late bruhh

  • Ivan Moloboco 2 years ago

    I’ll be 2 hours early before the class starts

  • Konsep Dasar 2 years ago

    I’m sorry, english isn’t my first language,
    why don’t you include the l’hopital theorem?

  • Joachim Kellermann 2 years ago

    I watch your videos for relaxation

  • Eva Peterson 2 years ago


  • Frijheid& Justitie 2 years ago


  • Giwa Bosun 2 years ago

    Nancy is so beautiful

  • Pro Life 2 years ago

    Nancy is so good

  • Aayu Sehgal 2 years ago

    I don’t know why i am watching this.

  • Erika Soriano 2 years ago

    You are an angel. Thank you so much for making it very clear. You really care and it shows.

  • Jacob Mach Ayuen Malok 2 years ago

    your work is so cheerful to me madam..

  • Singgih Solution 2 years ago

    I like it

  • THE LAST SHINOBI 2 years ago

    When your favorite math teacher-ytuber explains math within 16 minutes in juxtaposition with your math teacher who needs a trimester!!!!

  • Ricardo Pereira 2 years ago

    I’m 48 , I’m medical doctor, my hobby: watch to Nancys videos on calculus!

  • Md Ubaidullah 2 years ago

    So cute n sexy today.

  • Md Ubaidullah 2 years ago

    I like your accent n beautiful dress in this video.

  • Mihlali Mahala 2 years ago

    Thank you soo much! You are so good at explaining.

  • Michael Strydom 2 years ago

    How does she draw backwards?!

  • Fredy M Guevara 2 years ago

    Thank you very kindly!!!

  • Omar Zaifulizan 2 years ago

    bruh this math teacher is distracting AF

  • Aditya Pandey 2 years ago


  • Retro Byte 2 years ago

    I really appreciate you Ma’am for your immense help to all our maths needs… You’ve also inspired me to make my own channel.. I’ve uploaded some more questions which could be helpful once you’ve learned from nancy

  • Kevin K Uanivi 2 years ago

    Hi guys …I’m from Namibia and currently doing my assignment for calculus and it’s distance mode I really don’t understand. I really need help
    +264815643800 (for WhatsApp)or … please help help help

  • Noah Norel 2 years ago

    L’Hopital’s rule is Limit’s kryptonite, literally

  • Cristina Mauri 2 years ago

    queen of math

Comments are closed.