AP Calculus AB and BC Unit 1 Review [Limits and Continuity]

► My AP Calculus AB and BC Ultimate Review Packets:
AB: bit.ly/KristaAB
BC: bit.ly/KristaBC
Before you watch this video all about Unit 1 of AP Calculus AB/BC, Limits and Continuity, make sure you get the study guide that goes with it (it's free!). The study guide is part of the Ultimate Review Packet, which I made to help you study for AP Calculus AB and BC. It has summary videos, study guides, and practice questions, for every unit, plus AP practice exams.
Skip to section:
0:00 - Introduction
0:56 - 1.1 Introducing Calculus: Can Change Occur at an Instant?
6:53 - 1.2 Defining Limits and Using Limit Notation
9:23 - 1.3 Estimating Limit Values from Graphs
15:05 - 1.4 Estimating Limit Values from Tables
17:30 - 1.5 Determining Limits Using Algebraic Properties of Limits
20:53 - 1.6 Determining Limits Using Algebraic Manipulation
26:46 - 1.7 Selecting Procedures for Determining Limits
31:19 - 1.8 Determining Limits Using the Squeeze Theorem
35:56 - 1.9 Connecting Multiple Representations of Limits
38:08 - 1.10 Exploring Types of Discontinuities
41:15 - 1.11 Defining Continuity at a Point
45:47 - 1.12 Confirming Continuity over an Interval
48:08 - 1.13 Removing Discontinuities
52:34 - 1.14 Connecting Infinite Limits and Vertical Asymptotes
56:39 - 1.15 Connecting Limits at Infinity and Horizontal Asymptotes
1:03:12 - 1.16 Working with the Intermediate Value Theorem (IVT)
1:07:14 - Summary
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out my website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
FACEBOOK // / kristakingmath
INSTAGRAM // / kristakingmath

[@kristakingmath]

Hey guys! This is a project I've been working on to help everybody who's taking AP Calculus AB or BC this year. Timestamps are in the description. I'll be releasing more of these AP unit videos over the next week or so. 🤓 I really hope you're all staying safe and healthy! ❤️❤️

[@nthabisengmaimela1281]

So happy to see you back, you have been such an inspiration and a great help during my university years

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This is incredible Krista, thank you! Anyone that is taking calculus, I always share your information. You helped me get through my college calculus also, your explanations and thorough demonstrations of what is at times a difficult subject to grasp and is much appreciated!

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Can you believe it? When I was very young, I tested out of College Algebra with Trigonometry. That was at a very recognized University.

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[@kristakingmath]

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We missed you teacher.

[@kristakingmath]

Missed you too! I hope you've been great! :D

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Omg, my exam is in roughly a week, and I think I'm gonna be okay now. I love how you covered everything, and idk if it was curriculum, but a fairamount of this was pre calc review. Thanks so much for doing what you don't have to do!

[@Tvfmsm]

Im already in my school's integral calculus course, but I wanted to refresh my mind and really enjoyed the videos! I have never seen this topic better explained.

[@daughteroftheking3220]

Thank you for this! I needed this for my upcoming Ap exam. You truly are changing lives. People like you do deserve a very honorable prize. Love your explanations. Thank you from the bottom of my heart! I can’t wait to use more of your videos as a number one source when I start taking more challenging math courses! You truly are the best!👏🏻👍

[@kristakingmath]

Thank you so, so much! I'm honored to be able to help! :D

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A teacher dedicated to their students. Sweet and to the point, no interruptions, but everything essential. This year I'm preparing to understand units ahead of time before i take the ap course in the year, and this helps me a lot

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This is seriously the best video ever. I am an upcoming junior taking Calc BC, and despite everyone telling me not to take it (oh, it's going to be incredibly hard; don't take it if you want your GPA to go down), your videos give me inspiration and an actual passion to learn more about Calculus! Thank you so, so much!

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Im in the same boat now, rising junior with everyone telling me not to take it, how did it go for you?

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Oh my goodness! An upload!!! It’s great to see you and I don’t even have math classes anymore!

[@kristakingmath]

Aww, thanks! Great to see you too! :D

[@stay2Disciplined]

Was That Sarcasm

[@user-dq2fc3dz8k]

Thank you so much for these videos! I barely learned any of Calc AB this year due to a bad teacher, and your videos truly saved me. I watched/studied them the weekend before the exam and got a 5! Thanks!

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Wow

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Krista, you're the queen of KZbin Calculus! Yours is a very important voice in on-line math education, one that is needed now more than ever. It's good to see you back at it, going above and beyond to help people master some very challenging math courses. I wish there were some kind of medal or award for people like you, those who give their time and energy for free so that others can learn and prosper.

[@kristakingmath]

So nice of you to say! I'm happy to help! :D

[@mattgagea]

Wow; I have my first test of the year tomorrow for Calc BC on all then limits and derivative things we learned last spring and thus far. I just wanted to say that what you've put together is amazing and is helping a heck of a lot with my studying. Thank you so much!!!

[@kristakingmath]

You're welcome, Matthew, I'm so glad this series is helping! Best of luck with the rest of BC! :D

[@muhammadhamzajaved9297]

It's good to see you, Madam. I hope you stay safe out there and healthy. Thanks for all the fun Math videos.

[@sethwicks84]

I took Calculus BC and got a 5 my sophomore year of high school and now im graduating soon and I've forgotten alot. Needed this series to refresh everything I already learned before I head off to college! Thank you 🙂

[@kristakingmath]

You're welcome, Seth! It's amazing how quickly we forget everything when we're not using it, so I'm glad I could be here for the refresh. Congrats on starting college!! :D

[@TheNickinator96]

I graduated last year with a b.s. in math and just want to say this is an amazing thing you're doing! My heart goes out to all the calc BC kids who are going to have to be taught Taylor series remotely lol

[@kristakingmath]

Right! Mine too, school is tough for everybody right now... students, teachers, administrators, parents. I'm hoping these videos can help supplement for anybody who needs them!! ❤

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Hi Krista, I’m a long time subscriber and great fan of yours. I’ve learned so much from you with Calculus, even though I’m a novice at best. I also watch Christine Breiner and Herb Gross MIT videos. The three of you are beyond brilliant; light years ahead of me. I thank you for your wonderful videos, Krista, but most especially for your kindness and patience with your superb instruction. You are wonderful, such a truly nice person. George

[@jenacook8723]

Oh I just graduated this last fall , watching this video now make me miss math classes , you were so helpful and sure always gonna be 🌹

[@kristakingmath]

Awww thank you so much, Jena! I'm so glad the videos helped, and congratulations on graduating!!!!! :D

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You’re excellent teacher! I’m student of Earth Science and Math in Mexico 🇲🇽. I miss you:) Greetings 💙

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Hey, I'm just a sophomore in high school taking this class, Your videos have helped me so much with Calculus. Thank you so much

[@alancontrreras]

WHAT A SOPHOMORE??!! u smart af ma boy

[@Chubbymank]

@@alancontrreras hahaha thank you, I’m a junior now but I’ve already taken most of the math courses. So to cover for this years course I’m taking AP Complex analysis

[@Vignesh27116]

@@Chubbymank It's just complex analysis not AP (APs are only the ones established by collegeboard). Bro trust me there's always some random kid in some part of the world 1 upping us. This dude in my school, sophmore, completed calc, diff eq, lin alg, and is doing discrete math

[@Chubbymank]

@@Vignesh27116 Junior now and funny enough there is this one kid who is a sophmore and he has completed more AP classes than i have and he is by far the smartest kid in our state maybe top 10 in his class for our nation

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@@Chubbymank From all the seniors I've talked to, I'm convinced at this point extracurriculars are more important. Junior year, 4-5 APs and really good ECs is far better than 8 APs and no life

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Your videos are SO HELPFUL! Keep up the great work! Thank you!

[@kristakingmath]

Thank you, Caleb, I'm so glad the videos have been helping! :)

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I can listen to your voice all day and all night, yet at the same time relearned all my college math. :) Thank you!

[@kristakingmath]

You're welcome, Qian! I'm happy to help! :)

[@James-md8ph]

So pleased to see you're still doing these videos on KZbin

[@kristakingmath]

Thanks, James! I'm hoping to be a liiiiittttllle more regular with posting than I have been! 🤣

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Glad to still see you are as active as ever Krista...this is Kevin from Barbados (we spoke many years ago when I asked you about how you started teaching online) thank you for your help back then.

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Krista, your videos and study guide materials are so much better than anything else on the internet. Your explanations are logical, concise, and entertaining. Your incredibly well-organized content saves me so much time and frustration. I intend to keep using your videos as I study upper-level mathematics in college. Thank you so much for your time and effort.

[@kristakingmath]

Wow, thank you so much, Katie! I'm so glad you've found the material so helpful, that absolutely makes my day! :D

[@lrobertiii]

Welcome back Krista!

[@kristakingmath]

Thank you so much, Descartes! :)

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I was gonna write something lovely but everything I thought about has already been written! ❤️

[@avaneeshmoorthy602]

thank you so much , I have an ap calc ab exam coming up and I plan on self studying , this helped so much

[@ulisesjaenalmarcha2861]

Great video to consolidate the foundations of calculus! In fact, all the series is really interesting. Continue like this!

[@kristakingmath]

Thanks, Ulises, will do!

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Big shout out to your guides, carrying me through AP calc!

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Mam trust me whatever higher engineering mathematics I'm good at is just because of you. Really I haven't seen any other teacher in my whole life who teaches like you. I appreciate your hard work and I don't have any words to describe my respect for you. Also keep uploading this precious content and u deserve much more than anyone

[@kristakingmath]

Thank you so much, harprett, I'm so glad I'm able to help! :)

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I have been watching your video since freshman! Thank you very much for everything! You are wonderful!

[@kristakingmath]

You are so welcome, I'm so glad the videos have been helping along the way! 🤓

[@MrVoayer]

So nice to have you back, Krista !!! Stay well and make more valuable videos ! You have my sincerely best wishes !

[@kristakingmath]

Thank you so much, Voayer, I really appreciate it! :)

[@ChadCarney-hu3du]

So much better than the AP classroom review people. They stop to talk every 2 seconds and it's very annoying. Your review videos are professional and actually useable. Thanks!

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I know right!??

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Welcome back professor 🌹🌹

[@kristakingmath]

Thank you, HISOFAI T! :)

[@mdbaseer361]

thanks for such great effort you put to simplify in a simplest form.

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Wow! It's unbelievable that you started teaching again on KZbin! Thank you so much.

[@kristakingmath]

You are so welcome, I'm glad to be back! :D

[@AV-rc5gi]

Have my 1st test for AP Cal AB on 2 days. This helps a lot in studying

[@catherinekaminski112]

Thank you so much for this review! Have my first test in a few days and I’m very nervous but your video really helped!

[@loveitgirl2202]

Note to self: 1.6 is a good reference to review 1.7 as well 51:06 to review piece wise functions Review 1.14,15, and 16

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you are such an angel!!! You explain so clearly and efficiently it's amazing

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SHE'S BACK!!!! :D

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Thank you so much!!! You don’t know it, but you helped me immensely with my calculus 1, 2, and 3 courses!! I got all As and you played a part in that so thank you :)

[@kristakingmath]

Thank you so much for letting me know, Antonio! You clearly worked really hard to make it through calc with those grades, and I'm so glad my videos were able to help along the way! :)

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[@kristakingmath]

I'm so glad you like them! :D

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Missed you a lot. So glad to have you back. Love you teach...

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Hello Krista, please continue making videos they're awesome!

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We missed you, Krista!!

[@kristakingmath]

Missed you too, haslan!! :D

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Learned more math from Krista than anywhere else in my Engineering degrees

[@kristakingmath]

Thank you so much, Mike! I'm so glad the videos helped!

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I am so glad I found this channel

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Omg you're back!! Nice to see a new video from you

[@kristakingmath]

Thanks, Ross! More videos are on the way! :)

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This video was amazing and I truly appreciate your effort

[@kristakingmath]

Thank you so much, Anubhav! I'm so glad you liked it! :D

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Krista, I've used your videos for Greens Thm / Stokes Thm...Double & Triple Integrals....thanks , as always you were a huge help. Btw, good to see ya around again :)...and you haven't aged a day ~

[@kristakingmath]

I'm so glad the videos have been helping! :D

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thank you so much! this helped me pass my unit test, really appreciate it!

[@kristakingmath]

You're very welcome, yas, I'm so glad it helped! :)

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taking my first quiz of the school year tmrw thanks for the review :)

[@kristakingmath]

You're welcome, Stark! I hope the quiz went great!! :D

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Excellent and a laudable initiative, Ma'am. I am extremely thankful. If there is any book in specific that you would recommend as reference book, please let us know.

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[@kristakingmath]

Thank you for always supporting me Kenneth! :D

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I do not know who you are, but holy moly, I am very impressed. I will be watching all of your videos. The way you explain concepts is concise and engaging. You have a new fan!!

[@kristakingmath]

Wow, thank you so much, Michael! :D

[@pastreas]

thank you for explaining this coherently you saved my life

[@kristakingmath]

You're welcome, pigeon, I'm so glad it helped!

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Welcome back. Keep up the great work.

[@kristakingmath]

Thank you so much, I will! :)

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Thanks I was able to do well because of you!

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Thank you I am currently taking up Calculus this will help a bunch.

[@kristakingmath]

You're welcome, I do hope it'll help! :D

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I wasn't able to study college due to financial but with these videos, now, I am more knowledgeable than to those who graduated from college. Thank you.

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I’m sorry about your previous situation and I hate to burst your bubble, but these videos are an overview of 1st year college calculus. College graduates learn this early among many other subjects so I wouldn’t say that you would be more knowledgeable than math graduates.

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this is SO SO helpful thank you !!!!

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Your teaching is as beautiful as you, Welcome back!!

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I really enjoyed your lectures. The series you are working on is very best. so thankyou you helped me so much to understand maths concepts.

[@kristakingmath]

I'm so glad you're enjoying the lectures! :)

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Thank you for the video.

[@kristakingmath]

You're welcome, Tripto! :)

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You just saved my life!

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Glad the calc master is back!

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The return of the King

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[@kristakingmath]

Thank you so much, Paul! Hopefully these videos are especially helpful right now while we're all adapting to this new reality. 💪

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Holy Shit. It's been a while...Like, I graduated and found a job since you last uploaded!

[@kristakingmath]

LOL, wow! That's crazy! 😂 But congrats on graduating and landing a job, that's awesome!! 👏

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I can't believe your back it's been ages😍

[@kristakingmath]

It HAS been! But I'm planning to upload more, and I think the new videos are going to be really helpful for a lot of people! :)

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Love the new visuals

[@kristakingmath]

Thanks! :D

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You are the G.O.A.T. PERIOD!

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Got a 3 last year in AB, trying BC this year, let’s hope I get a 4 or 5

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[@kristakingmath]

You're so welcome, Fatema, I'm glad it helped! :D

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WOW! WOW! Wonderful!!

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Im thankfull 🙏🏻 this will help me a lot

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It's been a long time, good to see your active again. Please introduce us to calculus III and IV And V.

[@kristakingmath]

Hey! I already have lots of multivariable calculus videos, which are usually covered in Calc 3 or 4, if you want to check them out! :)

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@@kristakingmath I'm doing it :)!

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Thank you for these great videos.

[@kristakingmath]

You're welcome, Matt, I'm so glad you like them! :D

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Excellent ! Thanks !

[@kristakingmath]

You're welcome, I'm glad it helped!

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You saved me from my Dif EQ class! :(

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SHES BACK .0.

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So sweet of you to put this for free

[@kristakingmath]

I'm happy to help, Muqsit! :)

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KRISTA!!! it's like seeing an old friend again I hope you and your closest ones are safe ❤️

[@kristakingmath]

Hey, Nicolás! Thanks for saying hi! We're staying safe and healthy, I hope you and your family are, too! :D

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I will take AP Calculus AB this year and this video helped me a lot to get a hold of the unit before going to class!

[@kristakingmath]

I'm so glad it helped, and I hope AB is going well so far! :D

[@welcometomcdonaldsmayitake2003]

@@kristakingmath Yeah it goes well. Surprisingly it started to make more sense as we go trough the units! :D

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​@@welcometomcdonaldsmayitake2003how was it?

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@@rahelbakr3532 I got a 4 with onlt 2 weeks of real study. Id say it was good

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Woah! Long time no see!

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Great explanation ❤

[@kristakingmath]

Thank you so much, I’m glad you liked it!! 💪

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Very good quality teaching video.

[@kristakingmath]

Thank you, Jennifer! :)

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Thanks very much it was a very useful lecture please do more lectures.

[@kristakingmath]

Thank you, I will! 🤓

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Outstanding video lecture.

[@kristakingmath]

Thank you so much! :)

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Trying to get a head start in July...

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That actually saved me thank you

[@kristakingmath]

You're welcome, Abdullrahman! I'm so glad it helped! :D

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Welcome back my favorite mam