How to Find Any Limit: Part 2 (NancyPi)
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- เผยแพร่เมื่อ 6 ก.พ. 2025
- 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: • How to Find Any Limit ...
For LIMITS at INFINITY, jump to: • How to Find the Limit ...
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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: nancypi.com
a literal queen she explains it so simply
Damn if I had known this channel at the start of the year rather than 2 days before exam I could've been a master of Math 😭
I wish our teachers explained things like this this is just superb I never thought these complex math things can ever be simple
You've made calculus looks like a child's play. Thanks for this amazing teaching approach
"You're going to be like a ninja..... but for finding limits at a finite value..."
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
And she was like stifling her laugh
Does anyone else watch these because of her amazing voice? She's like the Bob Ross of math
Andrew Fitch yes
LOL YES
Im just not good at limits...
@@princeofboredom24 Turn your weaknesses into strengths and arise as a Leader!
I do
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 =)
Hey did you ever get into dental school?
You are saving my life in calculus right now!
lmao she has a weird knack of uploading these videos at the most convenient times
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.
you literally saved my life and taught this in the most simplest form and explained every question I had. thanks :)
These videos are just so relaxing. I watch even when I know the content :)
I know what is so relaxing :)
it actually creates asmr!
2024 still watching this and enjoying it like it was the first time :) thank you infinitely Nancy :)
Nancy words cannot describe how much I thank you. From HS to now in uni you were always the person I knew would help my little brain. Kisses from laura
learned more watching this video than a semester and a half of university THAT I AM PAYING FOR! thanks so much
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.
You're a better teacher compared to my college professor 😭😍
College professors are souls from hell
@Random Autonomous Drone Pilot “America is the best :
No joke my professor is just linking to these videos instead of doing lectures. Idk why I'm paying for the class if its all here for free.
You do this in college? I’m doing this in 9th grade because my geometry honors class is too easy.
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 :')
This channel deserves way more subscribers.
Havent taken a math class in 8 years so my school has me start back at calculus. These videos are amazing. You cover the material well and the way you separate the material is very helpful. Thank you!
Nancy you talk so politely 💕💕
You're the best at graphs.
Nancy is a life saver
From now ur my new teacher 😉❤
youre the only channel i come to for help with math. you have all the material covered, and explain it so thoroughly. thank you!!!
knowledge is invaluable and this girl has helped me SO much already with my calculus 1 course in college and has explained everything in 1/4 the amount of time 10x more clear... AND covers the basic algebra enough that it has completely refeshed my brain on the topic lol it has been refreshing! I really hope I can find a video from her over everything i need for my calc course! The limit of how much I thank you DNE! I love you to infinity and back... lol
Saved again by Nancy talking about math with ACTUAL WORDS!!!!!
Nancy has a talent of making things simple to understand and remember! thank you!
plus she is hot!!!
Thanks again Nancy, I’m a limit ninja now due to your help! You’re the best!
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!
She doesn't write backward, the video is mirrored in editing. Her explanations truly are amazing, though!
@@jamesallbee30 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 :-)
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 :)
Howd you do?
Nancy, I am so thrilled you are back. You were missed immensely.
Currently using these as a refresher for my Cal A midterm. Thank you a lot!
Apart from your beauty , the content is really excellent . I stopped doing math as I finished my studies and currently I should do some other stuff but I took a pen and a paper and was working with finding out the limits. Liked the tips for finding out the limits. Anyway , I liked and subscribed.
Best
Wow!!! Wow!!! My problem has been solved just by watching part of this. I love it 💙💙
I watch this channel constantly cuz shes beautiful, has a ASMR voice, and is a great teacher.
I genuinely came here to learn limits,
and now I feel like a ninja !! 😋
Maths would be interesting for everyone, only if the teachers taught like her. THANK YOU
and she looks like Megan fox
I came at the video bcoz of your beauty and i watched it bcoz of your genuinity and credibililty
Thank you for the wonderful video! It clicked in my head after skipping forwards and watching 20 seconds of you explaining the limits of absolute value functions ^^’
*Love the videos! DON'T GIVE UP NANCY*
Nancy you the best thing that has happened to me, thanks for all ur lessons bruh helped me a lot
i have a calculus exam in 2 hours, thank you so much you're saving me
Here to become a limit ninja!! Thanks yet again, Nancy!
Thanks, bloke. She makes maths hella simple for common blokes like myself, mate.
This lady is great, thank you very much,you saved me from confusion,I love your videos
you are beyond my teacher even.i understand more when its you teaching.
Thank you for teaching what my teacher couldnt teach me in months only in 2 videos thanks a lot Nancy
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
Very useful strategies for most limit problems. Highly appreciate it. Thank you.
So sad, I haven't seen your channel lately 😢... I'm happy now!
THANKS THANKS THANKS I literally just watched this video and scored full on my quiz.
I wish I had a teacher like you when I was studying ''Limits''.
Thank you so much, Nancy, you have just saved my life!!!!!!!!!!!!!!!!!!!!
I want someone who looks at me like Nancy looks at Calculus :D Amazing videos, thank you so much!
Thank uuuuuuuuuuu so much u really helped me I'm studying with French at school but i learn maths with u
You are awesome!!!!!! I learned more with you than my professor about limits. Good Job Nancy
multiple hours stuck on one problem based on my school material, watched this and got it in less than 5 minutes
God bless you Nancy
you explain everything so well! thank u so much!
I love the way you teach, and thanks to your videos I understand musch better. Thank you
Just in time to prep for my Calc final! Thanks for the educational vids :)
you're a lifesaver! and you actually made limits kind of enjoyable
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.
Just in time for my Calculus class and test on limits. Thanks so much Nancy!
U ARE GREATER THAN OUR PROFESSORS ....
Yayyy!!!!! I’m so glad you’re here!!!!
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 .
Such a clean explantation, am your fan
I used to listen to lofi while studying. Now I listen to Nancy.
God she is something else I often forget I'm watching a math video
You are shooting my problems like Wynonna Earp. Thank you.
The rule at 6:21 is the coolest thing I've ever seen
Math Megan Fox!
She is too good I wonder why am I attending my uni rather than hers xD!!!
and she kills it again!!! huray!
Thank you so much🙏🏻, your videos are really helpful✨keep the good work ☺
Beauty and Brains!!! She is not only helping me with math but i think I'm in love!! Lol!
Thank you for the absolute Knowledge which is bestowed upon me to achieve my dreams.
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.
What a simp move my brother but its fine more room in firdaws for me :)
i love love love the way you explain everything slowly and made connections and how 'kindly' you explain everything like it's not "oh you should have learned this from precalc", "put in what you learned from the previous year" like shove it in your face if that made any sense. Thank you so much, you have helved me a bunch!
Thank you Nancy for your wonderful explanation. I study master in Math, I think you should put an open point even on the right of 2 because the function that you are using is not define at 2. Thank you again.
Hey nancy please teach us some applied mathematics for physics. BTW nice work👍👍
Glad to see u back
you're a perfect teacher .......it was a god lecture from you.🥰😍
your videos are the best! Ive learned so much
You make it sound super easy
Seeing that you teach somewhat abstract concept so easily as seen in this video, even with consistent pretty smiles in-between, makes me think i had been thought calculus by some elite buffons or rodents in the past which explains why i didn't understand but until now.
I really enjoy her tutorials
You are a Bob Ross of math
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.
في اي مرحلة لديكم في امريكا يعطى التفاضل والنهايات واللوغاريتمي نحن في سوريا ثالث الثانوي
I drank every time you said “OK”. Yipes!
Thank you Nancy ...you just made everything clear!!
you do a nice job on all of these !
U saved my test today
02:12 Trick :
Multiplying with the conjugate...
2-term x by the same, only the sign in the middle changes
this is helping SO MUCH!! Ap calc test tomorrow
how the heck she writes inverted
She just writes normally and just flips the entire video in the process of editing
Thank you very much,May God bless you, atleast I can now understand the way limits are done ,well done 👊
for 5) square root, if you plug in 8 it actually doesn't equal to 0 but root 6 because root x+1-3 when you plug in 8 becomes 8+1-3=6 so just the denominator is 0 but we still have root 6 which = 2.4.
I learned, at the same time I loved you🥺🤣
Wow I love your videos I wish you the best!! Your videos are so understandable and helpful!!!