Introduction to Limits (NancyPi)

MIT grad shows what a limit is, how to read the notation, what it means on a graph and how to find the limit on a graph. To skip ahead: 1) For how to understand limit NOTATION and the CONCEPT of the limit, skip to time 0:34. 2) For WHICH WAY TO LOOK AT THE GRAPH to find the limit, including when to use the X and when to use the Y, skip to time 1:52. 3) For ONE-SIDED LIMITS notation, including the LEFT-SIDED LIMIT and RIGHT-SIDED LIMIT, skip to time 7:54. 4) For how to understand limits where X APPROACHES INFINITY or negative infinity, skip to time 10:24. Nancy formerly of MathBFF explains the steps.
For HOW TO FIND THE LIMIT (at a finite value), jump to • How to Find Any Limit ...
For HOW TO FIND THE LIMIT AT INFINITY, jump to • How to Find the Limit ...
Follow Nancy on Instagram: / nancypi
Twitter: / nancypi
1) LIMIT NOTATION and WHAT A LIMIT MEANS: You can read the limit notation as "the limit, as x approaches 1, of f(x)". This means "when x gets very close to 1, what number is y getting very close to?" The limit is always equal to a y-value. It is a way of predicting what y-value we would expect to have, if we tend toward a specific x-value. Why do we need the limit? One reason is that there are sometimes "blindspots" such as gaps (holes) in a function in which we cannot see what the function is doing exactly at a point, but we can see what it is doing as we head toward that point.
2) HOW TO LOOK AT THE GRAPH to find the limit: a) For a removable discontinuity (hole), b) For a removable discontinuity with a point defined above, and c) For a normal line. When you're finding an overall limit, the hidden, implied meaning is that YOU MUST CHECK BOTH SIDES OF THE X-VALUE, from the left and from the right. If both sides give you the same limit value, then that value is your overall limit. In our example, to find the limit from the left side, TRACE X VALUES from the left of 1 but headed toward 1 (the actual motion is to the right), and check to SEE WHAT Y-VALUE the function is tending toward. That y-value is the left-hand limit. To find the limit from the right side, trace x values from the right of 1 but headed toward 1 (the actual motion is to the left), and again check to see what Y-VALUE the function is heading toward. That y-value is the right-hand limit. Since the left limit (2) and the right limit (2) are the same in our example, the overall limit answer is 2. If they were not the same, we could not give a limit value (see #3). IMPORTANT TAKEAWAY: For the limit, we DO NOT CARE what is happening EXACTLY AT THE X-VALUE and ONLY CARE what y-values the function is hitting NEAR the x-value, as we get closer and closer to that x. In other words, the limit, as x approaches 1, of f(x) can equal 2, even if (1) = 3 or some other number different from 2, or even if f(1) is not defined or indeterminate.
3) ONE-SIDED LIMITS (RIGHT-SIDED LIMIT and LEFT-SIDED LIMIT) for a jump discontinuity: as you saw in #2, to find the overall limit, you have to check both the left and right limits. Sometimes the left limit and right limit are not the same. If you get a limit question with notation in which the x is approaching a number but with a plus sign or minus sign as a superscript, that is notation for a one-sided limit. The minus sign means the limit from the left, and the plus sign means the limit from the right. IF THE LEFT limit AND RIGHT limit are NOT THE SAME, then the overall limit DOES NOT EXIST (sometimes written as "DNE"). Even if the left and right limits are different, you can still write the left-sided limit and right-sided limit values separately.
4) LIMITS in which X APPROACHES INFINITY (or negative infinity): Another "blindspot" is when x goes toward infinity or negative infinity. Since we can never "see" exactly at infinity (or negative infinity), we can use the idea of the limit to say what y-value it looks like the function is headed toward when our x value approaches infinity. If x is approaching INFINITY, TRACE x values TOWARD THE RIGHT (the large positive direction) on the graph, and see what y-value the function is approaching. That y-value is the limit. Note that the function may be approaching an asymptote. If x is approaching NEGATIVE INFINITY, trace x values TOWARD THE LEFT (the large negative direction), and check what y-value the function is getting closer and closer to on the graph. That y-value is the limit.
For more of my calculus and precalculus math videos, check out: nancypi.com

[@tanzinaeisha4882]

Can you please do videos for literally every topic in calculus? You're honestly the best! (:

[@primecrafts5308]

Iam confused where to see , To her beautiful face or on the board 😂

[@britneyferndx763]

i wish she would do this !

[@entelektuel.yolculuk]

I didn't know Megan Fox was teaching math online, didn't see that one coming.

[@takemein]

You can also check here. kzbin.info/www/bejne/l6HCaZaCYreWjtWTLimits

[@mallamarijayakar5727]

@@entelektuel.yolculuk 😂 true thoo

[@coryandrum]

This makes sense now, you did what my professor could not do in a hour and 40 minute lecture.

[@Nathan-iy3ug]

Yes unfortunately, yes

[@edessentials3206]

Your professor also couldn't help with your grasp of grammar. "An hour, not a hour". Bye🤨

[@coryandrum]

@@edessentials3206 you scrolled down in comments to make fun of people trying to learn; your cleary lashing out because your so pathetic and miserable. FYI No one cares but you lol, You should get some help.

[@coryandrum]

@@edessentials3206 ...Why would a math teacher teach grammer?

[@serayamartinez9950]

I like her pace and how she pauses so that we can absorb what she just said. These are the types of teachers I hope for. Thank you NancyPi :D

[@dhickey5919]

Thank you for the introduction to limits. One your special teaching techniques in many videos is covering common types of errors. Thanks for 'steering us away from the rocks'. In this video you also clarified the objective is the 'approaching value' of the limit and not where the hole may or may not end up. Great help.

[@AlanTuringWannabe]

I really appreciate how this material was presented in an easy to understand way. Your pacing was perfect and so were your examples.

[@evilum]

nancy, i wish the time you help us learn math wasn’t limited

[@HendersonDesign]

It’s not limited. You can watch her videos as many times as you want....

[@evilum]

issa joke

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amty yes you are tight

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X😅😹

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Hi

[@caomoletimoloi6565]

You sure are a lifesaver, Nancy. It is through you that my journey in math is SMOOTH. Even my two math teachers combined cannot surpass your tutoring skills. Keep up the tremendous work!!!!

[@KuchisabishiiYo]

This is my first topic I'm learning for a maths projects on limits. It's a challenge but understanding the concept really helped me.

[@yapibowler9544]

For me, you have the perfect lecture videos in KZbin ma'am! The discussion is highly commendable. The speed, the presentation, and all, are just so perfect to me. I hope you make lecture videos to all topics in calculus. I am really amazed with how you make calculus looks easy. Thank You!

[@kittyheart1432]

Thank you for doing this, Nancy! I'm just returning to college and it's been *some time* since I had high school calculus, which I am now taking in college. Thank you *so* much.

[@mgj989]

Studying Cal I for a summer semester and this really helps supplementing info and explaining it in a way that's easy to understand and apply, thanks!

[@mikey38632]

One thing I love about these videos besides the really great explanations and illustrations is the fact that Nancy is pretty much ALWAYS smiling!! She is teaching math and smiling all the time!

[@adityagope8392]

where is the smile ? all i can see it limits

[@Alex-ns6hj]

@@adityagope8392a limiting smile?

[@stargazer140]

No lie Iearned more from Nancy in 2:26 min in than I did math teacher on the whole first day of class. Thank you so much for all your help. =) hug emoji plus hearts.

[@user-yy3xd4vl8s]

I agree

[@jeffreycanipe1936]

You have such a gift of teaching and explaining complicated math in a simple way.

[@danichats8047]

Non-tradional student going back at 32 and had not had a real math class in ten years. Your videos are making all the difference! Thank you.

[@michelledudley5605]

Same here

[@rururu5877]

Goodluck!

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@@michelledudley5605 Same here hahaha and Im a nontraditional software engineer and I can agree with this!

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Same

[@danichats8047]

@@rururu5877 I graduated ! made a c+ on my calc final and got my piece of paper. Easily my worst class but I made it!

[@dumdum7099]

I'm so very grateful. All I can do to repay you is to watch every commercials. No skipping.

[@shazzykitawa7581]

never been able to understand youtube math videos, THIS HAS MADE EVERYTHING EAASY YOU SHOULD HAVE WAAAAAAAAAAAAAAAAAAAY MORE VIEWS thanks alot

[@randalthor8483]

Keep it up Nancy you're doing such a huge service to those of us who can't pay attention in math and need a good tutor!

[@hayfaahope9017]

Nancy, I hope you the best in everything you do! Honestly an angel.

[@visions3]

Great teacher!!! Explains it so well! I wish there were more teachers like her

[@jordan199311]

This has been SO helpful! I'm taking Calc 1 this year and HATE math. my professor explained it like it was "easy" but since i didnt understand the concept I could not figure out how to actually do it! This has been so clear!

[@mzwanelendubata6874]

I'm really impressed by your ability to pass on information...please keep these vedios coming

[@sthitapragnyadeshpande3321]

She makes limits so simple :) - I hated this topic when it was taught at school, but now, it all seems so simple and logical. Thanks a lot, Nancy.

[@Sjb2077]

Again, just brilliant. Nancy makes it so simple. Thank you

[@thanujasuraweera477]

Thank you so much for all the videos on calculus Math. It really helped me a lot when I was taking math 114 at university.

[@michelledudley5605]

Great job of filling in the missing dots from the text book and lectures of the course on this topic. Excellent supplement to the course material. It always seems like there is one small piece of critical information missing that hinders me from successfully working the problems from the course material.

[@ZukuseiStudios]

I use your voice to help me meditate, it is so relaxing, drops my blood pressure & I’m learning maths effortlessly as a bi-product, amazing , seriously is that voice for real? Truly calming...

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Wonder who's the lucky guy?

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@@AbdulH his name? Albert Einstein

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fucjkibng simp

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LMFAO nerd

[@user-tg1qi9ju2n]

One of the best math channels. Your explanation is perfect 👌. I got A+ in all math courses because of your videos. Do videos for all the topics in Calculus please that would be helpful. THANK YOU

[@enaiwam]

nancyyy i'm helping my gf study for her calc and i remember how much you've helped me when i was in college, so i'm revisiting all your vids to refreshen my memory. thank you so much! youtube university the best haha thanks for the crash courses!

[@josephatjosephat9109]

I'll be taking ordinary differential equations this semester, your lectures will be very helpful! God bless you Nancy

[@velona509]

wow!!!! Fantastic. The best explanation of a difficult to understand topic. She is absolutely the best. Thank you soo much for your help. Please keep posting more videos.

[@j.e._3304]

Great video! I love how you simplify things to help anyone comprehend it. You're a great teacher!!

[@TheAAZSD]

I appreciate your explanations, It's been a while since Calculus I for me, and for tutoring, I find your videos to be extremely helpful.

[@medinasadigzade8757]

Nancy, literally couldnt thank more. You are amazing!!

[@tomboytomgirl5356]

Thank you so much for ACTUALLY pronouncing what 'the official and technical reading' of an expression. I consider this of UTMOST significance.

[@birddogstudio]

Thank you Nancy. These videos are incredibly helpful.

[@HOLYLIFEIFY]

From the left of one to from the right of one back to the left of one. Well put! Terrill TC!

[@mathtips877]

Dear Madam, your way of explaining the concept is excellent. This is the way to make students to think and do better.

[@dhanya._.ramakrishnan]

This video was very helpful and easy to understand. Thank you very much, Nancy. You're the best!

[@jannatbansal9841]

Your way of teaching is osm...thank u so much ...respect from India

[@cassandrajavier7158]

thank u so much!! words cant expressed how grateful i am for your videos thank for sharing knowledge

[@muhammadzubair4223]

Seriously you are the best I watch your videos to clear my concepts

[@MrGallinavoladora]

A very simple nice explanation. Just I was looking for, Thanks Nancypi

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Your lectures pierce my heart with logic and love.

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😚😙😍😘😗👄💋💞💝

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i can tell you’re much too old to be learning high school math buddy

[@chrismorang2008]

Had to disable subtitles to understand it better

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Lmao

[@haillanadelrey5292]

I’m taking AP Calculus and your videos are going to help me get through the class

[@hannagrantoza786]

your explanation is crystal clear omg im crying

[@Vanillabean321]

Thank you!!! I was having a hard time focusing on my profs vids -but this did the trick for a quick review.

[@esraayassin4938]

You don’t understand how much this have helped💗💗💗

[@escuetahyrumnathanielp.10]

If you're my teacher, I'll be always present

[@danielcoughlan4400]

I have been helping my nephew with his maths and I could not figure this out. I have been staring cluelessly at the maths book. I watched less than 2 mins of your video and now I understand it all. Thank you

[@rajendrakhedekar9272]

I really liked the description below the video. You explained the whole thing there also.

[@FM-hm7wr]

I was looking for videos on limits and as as soon as I saw "NancyPi" a smile, or rather a grin crept up my face. I even liked the video before I watched it!

[@augijyotbali2131]

Ow boy i love maths , after this CLEAR explanation , im in tears .😭😭

[@anandprakash4740]

My these 12 minutes and 42 second are worth it . Thanks to this wonderful teacher Nancy . ♥️♥️😊😊

[@henriallou9316]

Thank you. That helped me. I'm taking calculus 1 and needed some explanation. I will definitely subscribe and watch more of your videos.

[@SergioArroyoSailing]

Classic! This has helped my out so much! Thanks for re-posting :)

[@ayedhassan1065]

thank you nancy ..really you have a nice way to explain and way how to let others follow your lesson

[@julie198]

You are the best at explaining mathematical concepts! Thank you for making these videos.

[@evanwilson4035]

Omg you have helped me so much in under 13 min Nancy thank you!

[@tristanramirez6419]

You're a lifesaver, thank you.

[@kaylawagner3295]

Just in time, Nancy! I just did limits in class an hour ago!

[@X-MEN21]

I absototally love how you explain math, please do a video on probability and/or statistics.

[@NiHaoMike64]

I would like to see videos about efficient implementation of mathematical functions in computer code (or FPGA logic), but I don't think she knows much about that.

[@TheBoyxhero]

Thank you so much! I am learning limits now and this video was very helpful.

[@fahdciwan8709]

i had to close my browser when my mum came in the room .... i mean, i was doing nothing wrong, just learning maths but u never know with these moms

[@hardekailawadi]

Same lol

[@Aditya-fi7vk]

from which country are you bro .

[@hardekailawadi]

@@Aditya-fi7vk India

[@Aditya-fi7vk]

I got a feel with your language , same here. mummy boli, "ye kya hai , maine kaha calculus , mom had some doubts ".

[@pakistanzindabad-xg2rw]

same

[@anandprakash4740]

In self study such kind of teacher won't me feel hopeless . Wonderful explanation , that's hiw the video of introduction looks like. 👏👏👏👏 and a lot of thanks .

[@lumatv7385]

You are perfect, explaining everything slowly 👍🏻

[@unknown-mn9wo]

your explination is honestly the best ty

[@bosskaur2206]

its the best video to exactly note about the limits attitude!

[@teshane8784]

Omg thank you so much Nancy for showing that potential in math has no limits.

[@mikegenco9646]

Your videos are great. I did find myself thinking about the form of the actual function. Please consider starting with the actual function before going to the generic functional notation. I would guess that older memory cells have less micochrondria and less leak channels for higher required activations. Lol I am 69 years and no longer have immediate access to all my knowledge, until the next morning. You are truly an angel.

[@_KLAZ_]

Very nicely worded and paced. Thank you so much !

[@melvinpaul8412]

You are amazing at teaching in a limit that we can understand the concept..So thanks..

[@dreewhispers9408]

a math teacher smiling, that's new one, really good videos keep going

[@yasminhosam5951]

You're so nice and you helped me A LOT really

[@aminesf6776]

Nancy The Best Math Teacher of ALL TIME

[@ririe1356]

Thank you so much for this video. You made me get a clearer view of calculus

[@mccohn47]

You are literally a GOD SEND TY

[@zarolive6858]

Nancy you are the best!!! you helped me so much, so many times., just outstanding! And pretty too!

[@AlbertRyanstein]

Your smile makes me want to brush my teeth again. haha. Thanks for some great videos, spending the next 2 months studying Maths before my Msc. in Artificial Intelligence, England

[@clarisfeliz3998]

Excellent explanation, I appreciate A LOT what you have done.THANKSSSS;)

[@lachikagreen]

I finished my homework in 10 minutes thanks to your limits videos. Please post more! 🤓

[@jaspaw.5473]

Thank you so much Nancy! My probelms are solved..... Will be following all the videos as am a math major 😎😎😎😎😉😉😉😉

[@johnbarlow7988]

Have you ever thought about allowing schools to make use of your videos for teaching? I have been in schools for more than 22 years. Your videos are the best explanation of basic math concepts I have ever seen.

[@ChicaneMedia]

I just finished my first online CALC class 30 mins ago and was kind of confused about limits. Thankfully I found your video and it cleared my misunderstanding of what the limit was. There were two limit answers like you said such as 3 & 4. The resulting answer would just be DNE (Does not exist). I also didn't understand how to find them at first until you said to follow the line from left or right to the point to calculate the limit. Thank you really for making these informative videos. Without them surely lots more other people like me would have not been able to understand this topic!

[@ahmedshabahat8786]

i love how u simle and teach really awesome teacher u are

[@zuhakhalid3139]

You explained very well Nancy. Appreciated 💯💯💯

[@dreamscometrue5013]

I am pulling a all weeker. and your the savior. feels like i am cheating when you make limits so easy to understand.

[@raphaelthal5809]

Great job, tks. My prof. has made learning limits a hell. That was so hard to understand that I have lost interest on it for a while. I had to learn it anyways as I should move toward calculus, so I started searching for videos. Thank God I stumble into your channel by chance :)

[@okiadventure6031]

You're an amazing woman! I hope you will post more videos.

[@brandonpearce8371]

Thank you Nancy. You got me through Calc 1

[@johnbarlow7988]

Have you ever thought about allowing schools to make use of your videos? I have had 22 years of school,and your videos are the best explanation of basic math I have ever seen!!

[@tomscott3]

so, your explanation of limits/equal signs right around 5:00 kinda backs up an argument i had on another thread. the limit of something is _not_ really equal to that thing, but is what that thing _approaches_ . without referencing euler's notes, you back me up quite nicely, thanks!

[@cynthiagonzalez8702]

Thank you so much Nancy! My calc class just began covering limits :)

[@charrr7136]

same here hahaha

[@maximbalakin5135]

Thank you so much for doing my teacher's job for free

[@aimeelu6298]

OMG! Thank you so much, Nancy! I really liked your video! It helped me a lot. :)

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I really love you, ur voice and explaination

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NANCY YOU ARE THE BEST OF THE BEST THING IN MY LIFE

[@jaapongeveer6203]

I bought the deMystified book but this explanation is easier to understand. Thanks You!

[@jenniferestrada2971]

you are the best!! very grateful, Thank you

[@WeendyBSS]

Thank you so much im in 7th grade, and i actually understanded what you explained. You are a wonderful teacher🎉