MIT grad shows how to find the limit as x approaches infinity or negative infinity. To skip ahead: 1) For a POLYNOMIAL or CONSTANT in the limit expression, skip to 1:56. 2) For a RATIONAL ("FRACTION") expression in the limit, skip to 8:49. 3) For something of the form (SINX)/X, skip to 23:01. and 4) For an EXPONENTIAL example, skip to 27:27. Nancy formerly of MathBFF explains the steps.

For LIMITS at a FINITE VALUE (not at infinity), jump to the video: https://youtu.be/nJZm-zp639s

Follow me on Instagram! https://instagram.com/mathnancy

Follow me on Twitter: https://twitter.com/nancypi

1) For a POLYNOMIAL or CONSTANT in the limit expression: the limit of a CONSTANT (just a finite number like 3), as x approaches infinity or negative infinity, will just be equal to that same constant number. For the limit of a POLYNOMIAL (such as 2x^2 + 2x + 5), as x approaches infinity or negative infinity, just focus on the leading term (highest x power term) in the polynomial, usually the first term. You can ignore all lower terms, because as x gets infinitely large (in either the positive or negative direction), the highest term is growing most quickly, and the lower terms will not affect the limit value. Then figure out whether this leading term will grow toward positive infinity or negative infinity, as x gets extremely large. For instance, if the leading term is 2x^2, as x goes to positive infinity, this leading term will also go toward positive infinity, and the limit will be positive infinity. If the leading term were -2x^2, the x^2 would go toward infinity, as x goes to infinity, but because of the -2, the limit is negative infinity. For X approaching NEGATIVE INFINITY, keep in mind that a negative number, to an even power, becomes positive. A negative number, to an odd power, stays negative. For instance, what if the leading term is 4x^3, and you want to find the limit as x goes to negative infinity? If you think of plugging in a very large negative number for x, the 4x^3 would still be large and negative because of the odd power. The term would go toward negative infinity, so you can write that the limit is equal to negative infinity.

2) For a RATIONAL ("FRACTION") expression in the limit: I show a shortcut (and also the official formal algebraic method) to find the limit, as x goes to infinity or negative infinity. For the SHORTCUT, there are three cases: 1) If the DEGREE OF THE NUMERATOR IS LESS THAN the degree of the denominator, then the limit is equal to zero, no matter if x is approaching positive infinity or negative infinity. 2) If the DEGREE OF THE NUMERATOR IS EQUAL TO the degree of the denominator, then the limit will be equal to the ratio of the coefficients of the leading terms of the numerator an denominator, no matter if x is approaching positive infinity or negative infinity. For instance, if you're finding the limit of the rational expression (2x^2 - 5x)/(8x^2 + 3x), as x tends toward infinity or negative infinity, the limit will be equal to the ratio 2/8, which simplifies to 1/4. The limit equals 1/4. 3) If the DEGREE OF THE NUMERATOR IS GREATER THAN the degree of the denominator, then the limit will be either infinity or negative infinity. For ex., to find the limit, as x approaches infinity, of (3x^2 - 2x)/(x + 5), instead focus on finding the limit of the ratio of leading terms, as x approaches infinity. So instead, you can find the limit of 3x^2/x, which simplifies to the limit of 3x, as x approaches infinity. Since 3x goes toward infinity, as x goes to infinity, the limit is infinity. NOTE: if x had instead been approaching negative infinity, the limit of the original expression would have been negative infinity, since 3x goes to neg. infinity as x tends to neg. infinity.

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

4) For an EXPONENTIAL in your limit expression (with a negative power): for instance, if you are finding the limit, as x approaches infinity, of e^(-2x), first rewrite the expression using the reciprocal instead of the negative power, so 1/e^(2x). Then it is easier to see what happens as x gets extremely large and goes toward infinity. The e^(2x) gets extremely large, so 1 over a very large number will head toward zero, and the limit will be equal to 0.

For more of my math videos, check out: http://nancypi.com

welcome back

Welcome back

Nancy is back! Yay!

I missed you math queen

QUEEN OF MATH

+

@Syd the Kyd –

Yes

WE LOVE A LEGEND

Shouldnt it be e ^1/infinity which tends to e^0?

I love how u explain things!

I love you Nancy! You are helping me through engineering one class at a time.

The most impressive thing, imo, is that she’s writing backwards. and always keep in mind that math is fricking mind blowing! i got up to college level maths and i still am in awe of how amazing maths are and science (which is the same thing… pretty much)

ow..thanks for the basic of limit..hoping for more from u😍😍😍

Lol Girl making videos about mathematic… … i cant concentrate on a one thing…

a limit on infinity?, hmm

Nancy>>>Keep helping us.God will bless you

i love you miss Nancypi!!!!!!!!!!!!

coz i know you helped me so much

Nancy. Euler’s great granddaughter. 😀

Yeah, to Euler little Nancy was always his number e.

You’ve been of great help

Nancy I dunno how to put into words how much I appreciate your videos. I just started taking Calculus 1, I’m learning about limits and continuity/discontinuity right now and your videos are helping so much.

very nice

love youuuu nancy <3 <3

Nancy 😐 You are so distracting :*

me too… i can’t focus… i tried my best to focus but she’s so gorgeous but we’re grateful for the tutorials :*

yeah but in a good way 😀

Unless you love mathematics more than girls

Yeah dude it’s rough. I want to learn, but I just have one thing on my mind when I watch her videos lol.

You’re back 🙂

This section to me was impossible to understand , but thanks to you it’s now almost like 1+1 #Queeeeen

but how is she writing backwards :p

I love your videos. They help alot! Have you done any on continuity?

I wonder if your equation is bottom heavy or top heavy😉😂 i jk i jk i kidd i kiddd, very helpful vid tho fr thankyou

very specific presentation… thank you.

Thank you so much! It was so helpful!

Nice way of teaching

Nancy thanks a lot. you explain so clearly, so easy to understand

Love you Nancy.

you are beautiful also your math is beautiful , the up the good work

I just started calculus and was lost beyond belief. This is the only thing that has made any sense for me 😀 thank you

Thankyou so much for this video. <3

very hot.

Thank you so much Nancy, i love you hahaha

VERY HELPFUL

thank you

Nancy, thank you so much!

WE STAN A MATH QUEEN

We stan a legend. Nancy saved me in pre-calc

You’re amazing! I wish my calculus professor taught like this.

PLEASE do continuity

Do some more limits.

Excellent lecture

can u solve more problems on limits at infinity where problems contains functions like logerthems

Does she writes from right to left?

That’s what I’m also wondering

No, she’s writing on glass, films from the other side of the glass and mirrors the video afterwards.

correct me if im wrong but, I believe they do not cancel they divide to one. if they cancel they would turn to zero if that would be the case we would be in trouble…

Wonderful

you are the best. TY NancyPi

thanks Nancy…….i like your lecture😊

14:00 ✅

Omg thank you so much, the way you put it is so understandable Thank You!!!

nancy pi coming in with that fancy

Hi @NancyPi thanks for ur outstanding videos. Can you explain Continuity of functions under the topic Limits n Continuity. Thanks in Advance 😊

Brazil loves you!

you are sexy

Thank you for your an amazing explanation. I’m looking forward to seeing more calculus lessons.

I want to marry Nancy Pi

Very angry

you are the best

Nancy your saving my ass in calc. I’m binging your vids! Amazing

Do you guys feel that she explains better than DR and teachers in University

Hell yeah

*S U C T I O N* I’m yoinking your playlist ty

Yes

No. She taught mathematics informally. Her notations and terminologies are not widely used in mathematics.

Definitely

I wonder how you write that way. Anyway, ur so pretty

I love u

Got it bad, got it bad, got it bad……

Thank you so much for helping me in math but I would appreciate it more if you drop your skin routine 💕💕

Now thus is what am talking. About

You are so beautiful . :*

These videos are so helpful!!! Thank you 🙌🙌🙌🙌

do you have to write everything backwards on that board?

Honestly, you have amazing content. Just keep it up

what if its the lim as x approaches inifinity of cosx over x?

wao sexy teacher

what if u have( 0/0 )or (Infinity/Infinity )or (-Infinity+Infinity ) ??????????????

0/0 is indeterminate means that limit doesn’t exist or you didn’t simplify enough. Infinity/Infinity is simply 1 and -infinity+infinity should be 0 I believe but you also have to make sure that you account for the coefficients in front of x

I wish my calc prof would have just explained it that simply, thanks for the video! More calculus please

very good

so for finite numbers sinx/x is equal to 1 and for infinity sinx/x is equal to 0?

i just got distract for something …..

Thank you so much ❤

You are Legend ❤

can u do continuity

I’ll be thanking you during my speech at my grad party

I have that infinte * 0 is undetrminde form

Thanks again, Nancy! You are so very helpful, and I appreciate all you have done.

thank you very much !!!!!

I like the funny squeaky sound when Nancy the wizard writes backwards fast. At last, a method of teaching math that keeps you awake.

I really appreciate the great structure you design to elaborate on this! it makes things more clear for me to understand.

how could a math teacher be so beautiful

you are smart girl teachers don’t often show their faces but u have Managed to do so

Hello Nancy.İ usually dont comment but I have to say thank you so much.This was a great help.

I love her teaching method she is unbelievable

Passed Calculus but..

failed no nut November..

Lmao

please do continuity

I discovered your videos today and my god, light bulbs going off. I’m in Calculus 1 and have been struggling with limits. Thank you so much!! Please don’t take these vids down!! Would you be willing to post a video about related rates? I’ll (try to) do your homework in exchange (don’t count on a good grade though). 🙂

NancyPi = The only reason im passing AP Calc

do u know i love u , u are amazing 😘

Thanks alot

I wonder what are these used for i cant think of a aplication for this, is it made just to torment students?

Thanks

I love u

Thank you nancy!

Nancy yo are so beautiful i will follow you to the Infinity. ♥♥♥

Geekin

simp

🤣🤣🤣🤣

What about 1/n^1/n limits goes to infinity l?

You explain limit better than anyone else! You’ve made this so simple to understand for me thank you for making these videos!!

Excellent, i really like how you explained Nancy…

You are saving my life for finals

beautiful lecture 😛

Thanks for giving guidelines

What grade have to study limit?

mam you are so cool

in maths

i love u

You’re beautiful

Your lesson > my “Professor”.

your videos are awful

DAMN GURL ROCKKKK IT

YOU ARE THE BEST!!!!!!!!!!!!!!!!!!

Maths is too easy if you have a teacher like her

Aacha ji 😂

I love math and pretty girl . Well , now I have both ! hahaha~

Nancy, what do you do for a living?

زينب سوتلج dis like

This was very well explained! Who else comes to her videos straightaway when you don’t understand a topic in the class? *.*

Hi Aymoreno, you asked six months ago ” Who else comes to her videos straightaway when you don’t understand a topic in the class? ” Well, I watch Nancy Pi’s Calculus Videos BEFORE going to class so that I will already know WTF is going on and so my eyes won’t glaze over.

I would come to her videos even IF I understood the topic in class

You are fantastic

You are so cute

The shortcuts were nice. Thanks!

How does the lim(x^2+2x+5) as x -> infinity equal infinity. Since that’s a quadratic wouldn’t there be an asymptote???

Hey!! I noticed a thing. Her facial expressions are a lot similar to Dina fitz titan. From attack on titan.

😶😐😐😐😶😶

Thank you for a very helpful video!

Dear NancyPi, please make some videos on Monotone Functions

Why u keep on smiling😭 so cute

Omg she is MIT grad

Lim x-> infinity of (sin^2(x)/x) = infinity not 0

Thank you so much, you are just amazing – I’m always blown away by how incredibly simple you present these topics.

Can you explain me calculations for e^-1.630

Thanks for this video! In 30 Minutes I understood what 6 Hours of Classes couldn’t achieve..

you are so sexy

Any way I love you💖💖💖😍😍😍😙😙😙😙

Good

Honestly we need more teachers like this in the world

The utter joy I feel when I see Nancy pop up after searching for the topic I need…

ⴰⵣⵓⵍ

SAME

@Ngozi Onuoha

212-657011748+

I always have problems with limits that why’d watch her video it helps.

@Usama rafieck 212-657011748+

Please take my prof’s job

Functions or expressions may have a limit at infinity but Nancy has no limit in mathematics 🙂

F(x) =-3x+(-1)^x/4x-(-1)^x as x tends to infinity

She explained how to find derivatives exactly as my Calculus teacher explained today

I wonder if he saw your video before class.

Probably not

Wow, you are so lucky to have a teacher explain like this

My teacher all the time just writes on the blackboard and then wipes

And am studying that shit at grade 12th.

Same with me, I am studying this in 6th grade

Well guess what im not gonna need to study this shit anymore. Exams cancelled. Promotion granted😀😀😀

Came here to get help for my calculus test today. Instead I just fell in love

Yeah, it’s good to take a Cold Shower first so you can pay attention to what she is saying.

AND she could do your math homework for you!

ChiCharrone Jr Cringe

I learned calculus and fell in love!!

I got the same feeling every time I watch some of her math tutorial videos.

NANCY UR THE BEST THANK YOU FOR SAVING ME FOR THE 1294702397Q TIME.

is she left handed or right handed?

Thank you !!!

GREAT VIDEO! Super helpful! 🙂

thanks beeee—utiful

i wanna be your infinity <3

Can you find the limit x[x]/sin|x| x approach to 0

I love you from India,,, loves your teaching style,,,,ur beautiful,,,,i love you madam,,,eyes are beautiful

Bhai padhai kar lo par laundiya toh bohot sahi hai

Your voice is just a relaxing drug

She looks so confident and look how focus she is while writing ….that everything seems so easy…

I love math now

Magnificent!

Your very courtious Nancy !

dude she is so pretty

What if my rational doesn’t have any exponents?

Thank you so much! I had my doubt totally cleared because of you. Well explained with fun ways to learn!

THANKS SO MUCH DEAR TEACHER NANCY FOR SHARING YOUR MATH KNOWLEDGE. GREETINGS A BLESSINGS FROM SAN JUAN DE LURIGANCHO, LIMA, PERÚ.

who will win? nancypi or a $200 calculus textbook written by a multimillionaire stanford professor?

nancypi wins. every time. stewart is garbage

Thank you for your help. My book on h.w. examples and class lectures do Not cover how to solve these problems and its gets really frustrating trying to figure it out on my own. God Bless

Nancy is the freaking BOSS of calculus. MAD PROPS

i love the way u teach,,but beta parda kia karo

you teach so well but you also so beautiful sometimes i dont concentrate on study …..i started staring you during lectures…. you are distraction for me but you r even too a good teacher

salute to you……

Tumhara dimag v naughti American se sna hua hai ky ??🤣🤣😂

Can’t you be my math lecturer, you’re amazing and thank you for the videos it really helped me !!

She is so beautiful 😍…..

be in your “LIMITS” 😉

She’s got it all….writing backwards? Master of mathematics and very easy on the eyes.

Yeah, that was discussed in another video and some smart guy pointed out that that she was probably using Video Editing Mirror Image to flip the glass.

When the infinite is a subset of predictable finite, that is eternity. And to find the limits of subsets with in eternity just try out synthetic analysis too

Math… simply beautiful!

Thanks

fucking legend

limits(rigorous approach)?

Miss please do a video on continuity.

Nice tutorial on a tricky topic.

I wish these kinds of videos existed back when I was in college (1980, give or take.) I would have done much better.

Yeah, but back then it was a War about the Best Textbooks. but, yeah, Information was different in those days. To KNOW anything back then, you had to subscribe to some Specialty Magazine (Mathematics Magazine) or join a club. But, yeah, you just couldn’t Google anything back then. You knew or or you didn’t… researching anything was like climbing Mount Everest without a sherpa.

Did she learn to read and write backwards just for the sake of making convenient videos for us?

We went over that in another video and some really smart guy told us that she must be using the Video Editing Software to flip to mirror image so we can read what she is writing from behind the Glass.

mathematics made simple. Nancy in my best math Teacher

Thank u so muchhhh……infinitely

Please teach in hindi from india

Very good

I watch this channel just to see her…soo charming..

0(∞) is indeterminate

Hi Drin, you say “0(∞) is indeterminate”. Really? Do you have a proof for that. My intuition is that if you have A(B) and A is Zero and B is any magnitude, then the Product will be Zero. And Infinity is simply a Magnitude, that, yes, in indeterminate in itself, BUT we are really CERTAIN about Zero, aren’t we? It is a case where once we know that that A is zero, the Product is already Determined and we can ignore the Value of B. Doesn’t that sound right to you?

@Leo Volont We know that 1/0=infinity so 0*(1/0) = 0/0 (0/0 – indeterminate)

So for rational expressions limits to infinity are the horizontal asymptotes?! 🤯🤯🤯

Hi MrREmm, You say “So for rational expressions limits to infinity are the horizontal asymptotes?! ” Well, almost. If the Denom is a higher power than the Numerator then the horizontal asymptotes will be at Y = 0. If the Num and Denom powers are the same, then the Horz Asymptotes will be at the Fraction described by the leading coefficients. But if the Rational Expression is TOP Heavy, that is, if the Num out powers the Denom then you WON’T get a Horizontal Asymptote. There you have to Simplify your Leading Terms of both the Num and Denom and see what kind of Waveform that gives you (if the difference between the Powers is 1, you will get a Straight Line with a Slope, if the difference is 2, you will get a Parabola, etc.)

Amazingly clear and easy to understand!

Thanx Nancy:)))) Keep helping us

Hi mam you have any short cut about area of triangle when sides are given please give your phone no please

I love u Nancy u r so lovely Thanks

Really great video ,good explanations!!!

because of your beauty haw can say and I canot say haw beauty is you are haw clever is you are i cant say

Thank you triple thousand hundred

24:00 how did it disappear?

Ah yes the magic of editing

Thank u very much ..

Miss Nancy

Love from manipur

I wish ı had math teacher like you then ı would be a professor🤥Come to Turkey,Come to Adana.

How can you write?

Hi Piseth, you asked “How can you write?”. Well, we discussed it another one of her videos and decided that she write from behind the glass but then uses the Video Editing Software to flip it to Mirror Image. That would sound about right. Oh, when doing Selfie Videos, always check to see whether you look better natural or in mirror image… there is a difference. For instance, all of Tom Cruise’s movies are shot in mirror image because he thinks he naturally looks short and ugly.

Thank you Nancy!

A tangente betwen 2 hyperbole plz

How did i fit thé camera as Well as mirror plz

You can do the Mirror Image with just the Photo Video Editing Software. A lot of people use it because they think their facial symmetry looks better in mirror image.

Hi Nancy, I learned something today about your name. I was putting off studying Math (its summer break and next semester is Calculus I, but I’m using you to get a grip on both Calculus I and Calculus II). But, yeah, I was reading one of the most famous Novels in the English Language: “Clarissa” by Samuel Richardson, a novel written in the form of Letters going back and forth between the main characters. Well, Clarissa’s (Clary’s) best friend is Anna Howe, but whenever Anna gets particularly ‘saucy’ the name was becoming ‘Nancy’ which was a kind of a WTF moment for me because, you know, where did this Nancy just come from. So I looked it up and it turns out that Nancy was the diminutive form of Anna and only started to be used as a proper name in the 18th Century… so the change was happening even while this fictional Anna Howe was both Anna, formally, and Nancy, when she was being ‘saucy’. Cool, huh?

Intresting topic and good explanation. Thank you!

Thank you very much!! Great explanation

Babes + maths: I love lifeeeeee

you are right handed…for a moment i thought you were lefty..

i will find your limit and we will go until infinity

Great work nice lady

I really wish you taught at my university.

that last line for likes seems to suit well with every topic . Thank you mam.

I would have never know that infinity had a limit without you Nancy…

Kinda hard to focus… aghh.. I’m kinda attracted to gorgeous intelligent instructors.. I swear I won’t fail my exam, Madam =~=

She smiles after she writes down on the glass panel

how to find log limit values?

Keep going, I am in love with your videos. You make it seem so simple and explain it in the most basic way for everyone to understand. Thank you so much.

i love u

Really curious how she writes in reverse, or is she? someone explain pls

Right handed, normally, on glass facing a camera on the other side. Then just flip left/right like a lot of webcams do anyway. The fade-out effect of just the text is a little more complicated but I figure out at least one way she might be using.

@Veritas et Aequitas how does she have a piece of glass at home

Thank you so much for your help! I love you as much a Khan and more than Richard Rusczyk!

.

Every time you are showing but not showing…

O my gosh, I love you <3

How will i be determined if the function grows “Faster Than”, “Slower Than”, or “Equal Too” ?

than another function? Well if the two functions are equal then they grow at the same rate. For faster or slower it’ll depend on what x is approaching or what the function is, I think.

YES THANK YOU IM IN CALC AB AND I REALLY NEEDED THIS LOL

17:50 When I use a graphing calculator to graph the function (3x^2 – 2x) / (x + 5) a vertical asymptote prevents the graph from approaching -5 so the limit of that function as x approach -inf must be -5?

that -5 is not included because if you use it, you would be dividing by 0, and you can´t do that. The answer to a limit represents a Y value not a X value.

i don’t feel like im learning anything new… i know all this already but im still watching 🙁

i want you to be my mommy T_T

Can’t focus hahahaha

she is really awesome, so brilliant…

Thank you for this

You have really cleared my confusion.. please never stop making these videos…you are helping the confused souls in class make it!!!!

Hey i m from india i know a same teacher like her as pretty as intelligent.

Her channel is” neha aggarwal mathematically inclined.”

Hope u guys will get something from her also

Neha aggarwal

She is from Vedantu team right

Your videos are always so helpful! Thank you so much!

is she writing backwards AND doing calculus?!

I think she flips image so it looks normal to us.

@I lost my pointer lmaooo that makes much more sense

I usually never comment on youtube videos but I just had to say how much this has helped me. THANK YOU SO MUCH and never stop making math videos!! 🙂

Why cant I have a professor like you

In case anyone needs it, here is the missing link for ‘Intro to Limits’

I need her in my life. So I will understand nothing she talks about.

Thank you so much! Big help!

thank you so much this video so helpful ,but i have confused about infinity times zero how is equal zero ,and we know this quantity is undefined

I don’t know if this will help, but when I first learned about multiplication, I was taught as a number (a) and however many groups of that number (b). So 5 times 4 would be 5 groups of 4 (or 4 groups of 5). I think of it the same way with infinity and 0. You either have unlimited groups of 0, which is still going to equal 0, since there is never any value. Or, you could have 0 groups of infinity, in which 0 groups of something just equates to 0. Hopefully this helps!

Thank you! You’re amazing!

I hate Math but I don’t know why I’m here ……✌😁😁✌

how about logarithm? i have question with ln in it. T.T

Plsease make video on complex no plsssssssssssss mam I hate it I live in a fear of complex no and my exam in January plsssss I am your fan

Lan olum bune daş bide bizim limit anlatan hocalara bak 😒

Fantastic!!! She’s cleared up a MASSIVE confusion I’ve been harboring since my first semester at engineering school

*so did she write it forwards or backwards…*

see this why I can never pay attention in class

She wrote it normally the camera just flips it because the camera is like a mirror

i love u

Hey! Thank you for a very helpful video. I was just wondering how the limit of x*[(sinx^2)/x^2] as x approaches infinity would be 0. The expression simplifies to infinity * 0, which is undefined. So would the limit not exist?

Anything times zero will become zero. Approaching infinity is like a huge number, and a huge number times zero is zero. The expression might simplify to infinity * 0 but the denominator is still 1 so it isn’t undefined, it’s just zero over one, which is zero.

18:25 “use algebra! *hopes the idiots she is talking to know what that is*” :D. These videos seriously helped me. Thank you and keep it up.

do you write backyards?? great help thank you

You r AMAZING!

your explanation is very clear.

Related rates? That would be super helpful!

Finally I concentrate in study

Great

Great video btw, it appears as if you’ve taken an infinite amount of antioxidants, exponentially and nonstop.

My business calculus ass gets so confused when these sins and Es come out.

Thanks again Nancy! I always like how you simplify everything.

Thanks a lot mam .you made it easy to understand the limits for me. I waiting for more videos from

You.I expecting video on complex number

If she taught these concepts this slow the class would be behind. I mean this is a good explanation but University professors can’t take this long in explaining a concept

Hloo I like that video

Please make more

Can actually use L’Hospital’s Rule for finding the infinity limits.

Your method helps too. Thanks.

Thank you so much… your videos are so clear and you nail what a lot of people would like to find answers for in such a godlike way…

Are you writing this all backwards? That’s pretty impressive

Oh yeah i just noticed😮

@mad face I actually looked it up. She just flips the screen after she’s done recording

My GOD I can’t focus I always get destructed by her smile

Like bro ..lmaoo

this is only true for horizontal asymptotes right? these rules wouldn’t apply to the vertical asymptote at all

You’re awesome

Thanks you for your videos. It is really helpful for me as well as for the others.

hey boo, whats yo insta… let me jump in dem dms tho… we can study clac and have fun … if u catch my drift

why lim exp negative X when x go to Xinfinity is +infinity

(NancyPi) thanks for the volunteer help you are outstanding;

guys let us reach her 1M subscribers.

U r too cute I sometimes get distracted by your smile :):);)

OMG, she feels the mathematics!!!

I am just getting lost in her eyes…

Ok Nancy nice going great job and looking cool

Nancy the Math Princess who rescued me from an F in calculus

Same here.

Shoutout to you❤✊🏾

how does she write like that

Finally found a video that relaxes you and gives you a headache at the same time 😀

Thank you 💕

I remember when she was barely starting out, because that was the first time i failed calc….

Nancy, if you are reading this please just know I am so grateful for your videos… so many difficult concepts explained perfectly… Thank you so much!!!

Youtube commentators have no limits!

The best mathematician

God bless you

Thank you, Nancy!

Your explanation makes things easier!

Hey love from India

Thank you ❤️

the utter joy when i see nancy in my sleeep

Who are the 72 people that disliked this at the time of writing this comment? I need to have a word with them… >: )

The most beautiful MATH teacher I’ve ever seen.😍

What could I say more than thanks? Thanks a lot

you are very good dear you just make it simple for me.Thank YOU Nancy

How can anyone concentrate?

0*infinity=¿

SUMMARY: Anything over infinity = 0.

For those who have test tomorrow and don’t have 30 minutes. You dont need to know anything else.

Thanks for reading

Nothing else? You can also get inf, neg inf, undefined/unbounded, etc. Or ANY ratio! You still have to apply logic, and if your professor wants a REAL i.e. mathematical proof, yer boned.

If she takes classes, no guy is Missing a single lecture

Wow! This is great! You are the best mathematics teacher ever

Hey can somone please help me find the seloution step by step

Lim X–>+inf x^2ln((x+1)/x)-x

Thanks mam…love from india

i am very grateful to you

thanq

thank you very much

Love u <3

I feel very calm and relaxing watching her videos. PLUS, I might be even able to learn something.

Does anyone know how to solve lim x→0 1/(2+3/X)?

I want some explanation please

And with the same equation as X approaches infinity

I did it already but I will rewrite it

lim as X approaches 0 (1/(2+(3/X))

@Franklin Okeke the answer is 0

Did you just substitute or use the transformation rule

Because sometimes L’ Hospital or transformation rule can give you a much accurate answer as substitution.

Your answer is correct tho

I wish I were in high school or college now.

Dont worry NancyPi… No one is thinking dirty when you say HUGE, Large, or big….. buuuuuuuuuut the hand gestures on the other hand…. lol those probably more so…… it was rather quite cute watching you holding back your laugh. But thank you for the video it helped me find a answer to my problem…. along with some entertainment.

Please do continuity

Can’t Concentrate and Don’t know where to look at

You did a better job of explaining this in 30 minutes than my professor did in 80 and my textbook did in 20 pages. This truly highlights how vital proper teaching methods are for the students’ comprehension of the material. Thank you!

Wait hold up for the algebraic way of solving limits at infinity, 0/2 is undefined right??

That is equal to 0

The limit of her beauty is does not exist.

Lets hope I pass my Precal Honors Final tomorrow! Thanks for the help Nancy!

The math Gods are good. They have given us this beautiful and highly intelligent professor. Thank you!

You look alot like my crush Jasleen kaur gill

in exponential portion i think u left the 2 number….where is 2

I could cry. Thank you SO much!!!!!! #STEMINIST

Such a math geek!!!

I need this kind of teacher in math class .. 😂

Great video, however I would have added a tidbit that these limits find horizontal asymptotes, with your 3rd type N>D finding an oblique through long or synthetic division.

ur hot

ⴰⵢⵓⵣ ⵏⵎ ⴰⵡⵍⵜⵎⴰ 👍🏻💗

lim -x^2 with x->inf would´t be +inf, once -x- is +?

u look hot

U looking like Norha Fatah you are so beautiful…

Excellent! I love your videos. Thanks for sharing with us your knowledge.

you’ve saved me, ty

not gonna lie, its hard learning when the teacher’s hot 🔥

thanks to your help, i can slide through my hw. saving myself hours of agony.

I think just me and you who are new to see this video lol

24:00

sin(x)/x = 1 just in case if the limit approches to 0 ???

Yes

it makes me very angry ! what does infinity really mean? very large or uncountable/unending ?

It’s a symbol for something thats unending, but it’s not an actual number

I’m in grade 12 right now and ever since finding this channel, I’m FINALLY able to breath and study knowing that I understand what the teacher is talking about. I’ve watched all the videos on the channel (this is my 3rd time watching this vid) and I’m finally confident that I can do this. I have a test on limits tomorrow so wish me luck!!!!!

how many of you just clicked the video because she is cute❤🤣🤣🤣!!!!!!

Thank you <3

Thanks, I love the video so much that I click the bell notification option

Your lecture is highly commendable. Thank You!

I think she explains better than the others. Thanks Pi

Thank you sooo much for this!!! My teacher is terrible and has no idea how to explain things to us. I always end up having to go to someone like you to figure it out! 😂

Wish I saw your channel before having my Calc class 💀 I died like 7 times during this topic

you explain this great your face is kinda distracting tho

i really love the way NANCY explains

tnk lot mam

infinity*0=undefined…. why did you write 0 at 27:04 ??? I am confused

Most beautiful educator in the world

Nice

I was trying to recall the topic to help my son whose school is closed due corona pandemic and I went through all her limit vedios in one go . Brilliant .

you have boyfriend?

This is making Maths very intersting.

When ever it comes to searching a Math help I remember this channel.

Thanks for the amazing explanation Nancy

Please do a video about the integration and differentiation of sin cos and tan pleaasseee, also wanna go out on a date ? Also maby some stuff about the chain rule

Thanks mam

Thankyou very much for your videos you’re a legend

Beautiful, but you didn’t mentioned the type of the x is power to a value, like

lim (6^x-3^x)/(8^x+x^9)

beautiful and intelligent.. WOW

how am I supposed to learn when she looks like that

you do a better job explaining this than my textbook thank you for your channel please keep making these videos

At 5:45 to 6:15 we can explain this better

You explain Excellent… 👍🇺🇸 But you are confuse with the – & + signs, why they are here?

🇮🇳… we can make this more friendly to understanding

Nancy, you are awesome!))

I like the way you explain.. So relaxed.. Beautiful and talented teacher … Amazing way to teach.. Beautiful smile..

whoever dislikes this is gay

I wouldn’t recommend that you write equal to infinity for the first question or equal to negative infinity. It’s better you write an arrow to show that the limit approaches infinity or approaches negative infinity.

I think she has to write backwards for us to be able to read it

27:49 My reaction when i realize i have calculus exam tommorow!

I am feeling like crying!!! Why I find her today not before!!! OMG!!! Thank You Sooooo Much Dear<3

I like this glassboard studio🤩

There is a great pleasure in madness which only madmen know.

Beautiful knowledge sharing. I always enjoy your explanatory steps. Big thank you

Very nice explanation ma’am thank you so much 🙏🙏

keep it up

how can i focus on your lecture when all i see is your pretty face(“,)

NancyPi, can you do a video on infinite series and convergence please?

U r my personal teacher, u rock

Helped so much, thanks!!!

Hi ms or mrs Nancy.nothing to say but you top. really👍

Hi, teacher

Really very interesting your teaching

You’re a life saver. Thank you so much for your content.

she is fit ! awesome

Very beautiful, fascinating and attracting lady.

plz help me …

lim x—》3 (x²-9)/(x-3)

its answer should be 3 according to your tricks but its answer is 6

Your videos are amazing. I am learning so much. Thank you so much for taking the time to explain math principles and laws with such care.

You’re great at explaning but can you also explain what you do to your skin? Because it’s glowing so much

Thanks soo much please don’t stop uploading

isn’t (0*infinitiy) does not exist?

Thank you Nancy for the videos about limits. I understand it better with you. God bless and more power!

your videos are amazing , so helpful !