Calculating a Limt By Factoring and Canceling

[@reganvdm]

Thank you so much for this. I’m an almost 30 year old environmental science major having to take calculus in my last semester. I have been trying for two weeks to grasp the concept of limits and I was recommended your videos. You have finally helped me make sense of just the basics to hopefully move forward this semester! If I had of seen these when you originally posted them I might have done better with pre calculus in high school and wouldn’t have waited so long to finish my degree 😂

[@patrickjmt]

hey! thanks for the kind words! and don't be intimidated, especially after a long break. some of my videos are a bit dated but the math is still good to go :)

[@jc_hz4196]

I remember this video when you barely posted like it was yesterday. If it wasn’t for you I would have never become an engineer, thank you for all the work invested in helping others.

[@sethjackson1143]

Thanks Patrick! Putting all your videos to use in studying for my calc 1 final.

[@bigstuff52]

As an old timer Patrick who had this stuff over 40 yrs ago-you would have been a great Prof for my Calculus classes.Tip of the hat to you sir.

[@91HPS]

If I wasn't such a broke student I would happily donate, I know you don't do this for money, but because you enjoy helping other people. Just wanted to say thanks so much for taking the time to help myself and other students with our calculus, really do appreciate what you do and it helps me actually understand calc. Keep it up!

[@furin121]

Thank God for you. :) I'm having such a hard time in calc because I didn't get a good grasp on doing limits (I thought they were harder than they actually are). I've watched about 20 of your vids so far on various items and can say my anxiety when facing my math homework has gone down tremendously. Please keep providing this information to me and others like me!

[@Pk1da]

You don't understand the level of thanks i'm at right now, honestly, i was struggling so much with limits, just looking at a limit i was confused, but this video really helped man, thanks a lot, and i like how you teach, too, it's so easy to follow along, keep it up man

[@Ultimita01]

I got a reminder today.. always testing my limits Patrick. Good reminder. I read once successful people do a few integrals a day. This reminder, reminds me I should attempt calculus again. If I can 'read' it again.

[@jennybarua3417]

why am I paying thousands of dollars for a teacher who teaches calc I that just goes on and on with notes that I don't understand, and this guy here is teaching me perfect limits for free in like 3 minutes.....wtf college?

[@kavan1773]

+Jenny Barua That's college for you. I decided to go to community college first to save some money, but honestly you can learn most of this stuff for free anyways. I don't think that's the point though, the point is to force you to learn and in the end you get a degree which is proof that you've actually know stuff. However, I've been finding that most college professors are really bad at teaching. It's best to get a tutor to actually teach the stuff you need to know.

[@thesage1096]

dont do that bob

[@JoseRodriguez-tx1qz]

Jenny Barua Smart people get a degree through KZbin. You should try that so you could save thousands of dollars from college tuition.

[@prospectcanada]

my teacher is East Indian, very difficult to hear and moves way to quickly during class. You're a life saver

[@patrickjmt]

no problem! i have lots of videos posted, and do not plan on removing them any time soon. : ) so all one needs to do is just look!!! : )

[@amanda2324]

Your opening problem is the exact same problem I need to solve in my homework.

[@tre-moon-dous6122]

lucky

[@amanda2324]

Syahrul Anwar I can help you with you want, I think. I aced my Calculus class, so your problems shouldn't be too difficult for me.

[@amanda2324]

***** Sure thing, lol.

[@heyyy3210]

PLEASE continue making these videos! For all the rest of the concepts of Calculus!

[@patrickjmt]

@jayronsoares i do not have dvds at the moment, but everyone keeps asking, so i may burn them off at some point. some videos are available for download via youtube for a fee

[@TheGrimRevenant]

+Sabrina Bosworth "0/0" is a form. So if you get a problem where you need to plug in a limit and the whole thing turns out to be 0/0, you need to use some algebra to change the problem(such as factoring it), then plug in your limit.

[@ruchieru]

Factor [(x^n)-1] so that it equals to: (x-1)(1+x^2+x^3+x^4+...+X^(n-1)) And since you have a (x-1) in the denominator as well you can cancel those two out. So you're left with the whole (1+x^2+x^3+x^4+...+x^(n-1)) term. And since x approaches 1, and whatever power of 1 is always equal to 1, then the sum of all those 1's to right to the end where you have x^(n-1) would just be n, since you also have a 1 at the beginning. So in essence it's really 1+n-1, which is n.

[@jaimeastorga2000]

NO. Intuitively, limits are the value that the output approaches as the input approaches something else. The removable discontinuity in the graph at x = 2 is a place where the graph is undefined. However, it is easy to see that, as x -> 2 ("x approaches 2") from either side, the y value approaches 4. Ergo, 4 is the limit of the function as x -> 2. This is true regardless of whether there is a missing point (removable discontinuity) there or not.

[@patrickjmt]

@jojogirl2008 you are very welcome ; )

[@AndyB1993]

They should teach L'Hopital's rule right off the bat lol.

[@patrickjmt]

yes being able to rewind is very useful :)

[@patrickjmt]

@katiemartin220 glad you like the videos! : )

[@sabrinabosworth3043]

This may be a dumb question but say in the beginning you plug in for x and you don't get anything over 0 or 0/0… would that be your answer?

[@patrickjmt]

when people first see these problems in calculus, they do not even know what a derivative is yet, which makes it a bit difficult to use L'H.

[@fifyfarisha9851]

thank you for sharing all thede knowledge, i've been saving and following ONLY you as i truly understand the way to teach. thank you so much!

[@TusksRUs]

You could, but this is a video explaining how to do limits generally - rather than specific cases (L'Hôpital's rule is only valid for when the limit gives 0/0 or infinity/infinity). But to answer your question, you could, in this case, the answer would still be 4.

[@stockingzxo]

Love these. My Calc teacher sucks. I now understand :) THANKS !

[@nanone1994]

Just started Calc first semester for my senior year and I am doing really gooooooood ;) yaaay love maths !

[@TexaninSpain]

great job.. I´ll be telling eveyone from QUMT class about you!!! Thanks for the help...

[@patrickjmt]

wonderful! you can now download them and take them with you! : )

[@emmanuelwinston8817]

Wow! no words! absolutely amazing!

[@deathdealer13cat]

dude u must be the best teacher ever. u should get money for this. are u a youtube partner

[@ry7ky]

Thanks man. I'm pretty in-adept at this so not sure if what I thought of can be considered correct mathematically, but what if you set the first equation equal to "n", then multiply both sides by "2-2", so "0n=x^2-4" then x=square root of 4 which is two. Again, the answer is right, but I'm not sure of the method. Thanks for your time :)

[@Greeneyehawk13]

this is great! Thank you! This is going to help me with my test in a few weeks

[@patrickjmt]

ok keep watching for free!! : )

[@patrickjmt]

glad it helps : )

[@patrickjmt]

jaimeastorga2000 is 100% correct

[@skyfaze]

@patrickJMT Congratulations!

[@orionbassmaster666]

god Patrick your a life savior , thanks for the videos and hard work , your simple approach simplifies alot of doubts , god bless buddy ^^

[@MegaBlackbomb]

you made maths easy buddy.... i salute you :)

[@vividmonkey]

@patrickJMT dude. awesome. you save my life distance learning life!

[@trueteen]

THANK YOU ! you make my life so much easier

[@Otanashi214]

I didnt know that until the last semester. it was easy and fast than do all those calculution, i think in the middle of the semester we learn the Derivative in college

[@TheToxicMegacolon]

Thank you sooo much Patrick!

[@Membersdesig]

Thank you Patrick

[@aparrotslife]

I appreciate you posting this video, Patrick! It is very helpul! :)

[@Bowenarro111]

Thanks for posting. These are so helpful!

[@richardbui63]

Thank you Patrick! Your video have helped a lot !

[@Kingpin745]

Dude why don't they have more instructors like you.. I frigging hate my professor wid a passion!!!

[@whitepouch0904]

@nevabagdown bcoz it is the factor of x2-4, and if you don't you'll get 0/0. and the limit does not exist

[@jojogirl2008]

THANKS SO MUCH! i appreciate ur videos so much!

[@warnexus]

great stuff! this video helped me refresh my memory!

[@neil9151]

damn i was too late to find this channel now i think im gonna retake my calculus next semester

[@shubhamsharma775]

Thanks for making these videos . What kinda pen do you use in these videos.

[@patrickjmt]

@EhancedTrance there used to be one on my old website: justmathtutoring dott com

[@ldahlbs]

i wish you got a penny for every time one of your videos have been viewed.

[@maidatulsarah]

why is the dot on the graph an open one? how do you determine if its undefined or defined?

[@SeleneDeVampira]

You are a saviour!!!!

[@accarl]

thanks a lot it really help me understand!!

[@patrickjmt]

that makes two of us :)

[@CassiusBenard1]

I paid $1000 to (not)learn what you just taught me for free. Donations will be sent.

[@ahmedkas3635]

great job ! its really helpful

[@kdwaechter]

So....limits are just a way of defining a point that is normally undefined?

[@psp785]

do u have a video for solving limits using tables

[@HypaXLink]

Outstanding.

[@navierstokes1]

Thank you very much!

[@cutiecool32]

@patrickjmt isn't the limit supposed to be -2? don't we put the answers in x-values?

[@misty348]

nice example

[@kritishasankla2190]

How would you find the domain of the limit?

[@hailatlantis]

Ohhhhh thank you thank you thank you. And thank you.

[@sfking00]

Dude i love you as much as one man can love another man without being gay. thanks

[@penitotx]

how can i calculate the limit of 1/h(1/square root of x+h-1/square root of x) as h--> 0 ? thanks for the time :D

[@ssk360]

ur vids are great,

[@patrickjmt]

@zoecastillo717 weep softly : )

[@patrickjmt]

@deathdealer13cat i am now a partner yes, so i get a little bit from the videos!

[@starflakeminicon4110]

You're a life saver T-T

[@agnibhbanik1082]

THANKS VERY MUCH!!!!!

[@2010FFF]

I LOVE U Patrick I will pass calc 1 thanks to you... I am studying for final

[@patrickjmt]

@orionbassmaster666 happy to help : )

[@smitarai9098]

Its for enginering or not

[@engineera5565]

when to use the limit of the function ???

[@DiegoH23]

a penny!! he deserves a dollar

[@harishli2020]

super explanation.....

[@lolita123lit]

thank you so much :)

[@patrickjmt]

@chickmitten : )

[@EhancedTrance]

do you have a donation link? I WILL gladly pay you.

[@Teshlakh]

can i use l'hopital's rule it's easier?

[@bhoskaronkar]

thanx

[@SevenMilliFrog]

that was awesome

[@Otanashi214]

if u uses L'Hospital Theorem u will get the same result which is 4 (2x)

[@doorfridgemagnet]

@patrickJMT The audio is now out of sync its all fuzzy

[@cubencis]

why don't they teach L'Hopital from the get go i wonder... thanks for the review

[@varghesekurian8666]

In this particualr case, I think factoring was much more easier.

[@patrickjmt]

@heyyy3210 tons of calc stuff out there by me : )

[@FcLS1Rx7]

Can't you just take the derivative of the numerator and the denominator? I believe its the same thing no factoring involved.

[@navierstokes1]

Could you help me with this question? lim [(x^n)-1] / (x-1)] x->1 The answer is n. I can't figure it out help please =)

[@wikkk16]

Great!

[@djwarped14]

i love you patrick -djwarped from philippines

[@whitepouch0904]

@karlkarlkarl1234 i think bcoz they have to factor or conjugate.

[@patrickjmt]

cause you have to learn limits before you can talk about derivatives, and derivatives are required to use L'H!

[@islamelbaz7232]

GOOD ...