# How to Find Any Limit (NancyPi)

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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 (https://youtu.be/v9fQ_QeCHpI) 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.

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: http://nancypi.com

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

• how did she get 2/3?????????

• Thank you! This is excellent.

• 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

• Plz try this method mam u can get the correct answr

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

• I like cutiepie more (marzia aka pewds wifey)

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

• hahahhahaha

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

• I wish I had a math teacher like Nancy

• Thank you From Morocco ❤

• First time realizing math could be joyful, love u

• Thanks Nancy 😍

• nice l

• Thank you NancyPi ..

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

• Nancy’s beauty has no limit. 🙂

• Father…. Mujhe isse padhna haiii

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

• you saved my life.

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

• 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

• 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?

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

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

• So straightforward. Brilliant!

• What would i do without You Nancy….

• Wow! Understood limits in class 8!!

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

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

• I think calculus is driving me to insanity

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

• Thank mam

• Would totally replace you for my Ex 😩💦👌😍

• Nyc mammm….. fabulous look of u studies

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

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

• 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. 😊

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

• foolish ASMR

• a big greeting from iraqi such a useful lessons

• 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.

• How is 2/3? but 3+1=4 and 3+3=9

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

• شكرا🌸💜

• 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

• Great Video!

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

• 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.

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

• 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?

• nice video….

• What I want to know is how she writes backwards

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

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

• 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!

• The way she says `Denominator´ 😍

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

• 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

• Same. Her voice makes me real sleepy

• 7:34 isn’t the limit 3i?

• I am in love …

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

• happy belated anniversary babes.

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

• You are just solving not explaing where did you get

• Thnx for all

• 6:48 who got it?😂

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

• You are great

• good teacher in mathmetics and good figure.

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

• She is awesome and Thnks for everything Nancy 😍🔥

• excellent job

• u are amazing

• I love you

• I will not be late bruhh

• I’ll be 2 hours early before the class starts

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

• I watch your videos for relaxation

• THANK YOU NANCY

• 🌲🌷🌲🌷🌲

• Nancy is so beautiful

• Nancy is so good

• I don’t know why i am watching this.

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

• I like it

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

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

• So cute n sexy today.

• I like your accent n beautiful dress in this video.

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

• How does she draw backwards?!

• Thank you very kindly!!!

• bruh this math teacher is distracting AF

• 😍😍

• 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

• 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