How to Find Any Limit (NancyPi)

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.

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.

[LeNguyen-imdm]

Nancy always looks calm and confident. She is not a loud person. She makes people feel comfortable.

[EvelynHernandez-gfqo]

My professor couldn’t explain in a week what you just did in 5 mins thank you 🙏🏻

[camd]

NancyPi you wonderful human being!!!

I have lost count of how many times you have helped me understand many difficult concepts in calculus that seemed so difficult when I learnt them in lectures... I’m so very grateful of your methodical and perfectly paced descriptions of everything you do. I always strongly recommend your videos to fellow students too! Thank you a billion! 😊

[wengsunlum]

A wonderful teacher. I love the way you write on the board - fast and swift, without wasting time. Keep it up!

[LuizMartins]

Math is a subject that stresses people out and your combination of calmness while explaining math in an easy way is perfect! Normally I need rewatch a math video 10x before I understand the concept, but with your video I barely need to rewatch them more than once. Please keep making more videos on college algebra and calculus. These free videos will pay you back. From here on out you can start your business by selling your content to schools.

[MrJandrade]

I'm 6 minutes into this video and I already learned more then I did in the past two weeks! She cuts through the writing of each problem and explains why things are what they seem!

[Natalia-ctue]

Okay you're actually saving my life here. I've watched sooo many other videos and couldn't understand what was going on, but you have such a great way of explaining and breaking it down! thanks a bunch! :)

[Sjb]

Thank you Nancy. I have watched many of your tutorials and understand maths so much better at the end of them. What is really helpful is you explain where and why common mistakes can be made . That is really helpful. Again thank you.

[ilyassentosa]

Your explaination was so systematic, clear and easy to understand. You're one of the best teachers in the world. Thanks👍👍👍.

[jesuisravi]

I really appreciate the way you expedite the explanations by speeding up the video at non-critical points.

[Dismythed]

You're an excellent teacher. I have watched a dozen introductions to limits and none of them made any effort to give an overview of what the math is doing, explain their terms or explain what was happening. They just launch into math as if the viewer is supposed to know everything already (That's not an introduction).

Thanks for this. It shows real intelligence and forethought.

[mitchong]

Thank You Nancy Pi! I just started Intro to Calculus, and my book mentioned limit laws. The directions from the book were hard to understand. You explained the different way in a clear, calm manner. Math is not as scary anymore, with your videos.

[elizavala]

OMG, you are a life saver, I am taking Calculus 1 this summer, and the professor is great, but he goes 1000 miles per hour when lecturing, therefore, thanks because I will spend a significant amount of time watching your videos.

[calvingroenewold]

I’d never miss a day of class if she was my teacher

[YM-CRAFTY]

you helped alot, this was way better than the numerous videos i've watced. There are several good teachers i learn from in youtube who teach physics and calculus but none of them made caculus (the derivatives and limits for me specifically) as simple as you did. Thank you very much, and i assure you that every student who watches your videos appreciates how you share the knowlede.

[oletunauyoma]

Thank you Nancy for sharing your knowledge with your viewers. I could not understand this for 5 months and now I understood due to watching 1 of your videos! You explained diligently, and you gave your all so thank you and God bless you abundantly for simply giving.

[suzi]

Absolutely LOVE your videos! I really like that you simplify every step and review small things that we should remember! Other videos usually jump past those details and I find myself lost! Your videos have saved me in CALC! Thank you so much! <3

[SmittyKat]

Nancy, you're doing the Lord's work here for real. I would've failed trig if not for you. Now I'm in calculus and I probably would fail that if it werent for you. Gonna be taking calc II next semester and then diff. Eq. After that. Counting on you! Lol

[damarisosterling]

Nancy, thanks so much for doing these videos. I fully understood how limits play now, and I'm so excited to check the rest of them. You are the amazing <3.

[soumiabr]

Your videos are kind of calming😂 maths therapy