❖ Calculating a Limit by Multiplying by a Conjugate ❖

[@raanoooshh9296]

There was an ad before this video starting and a voice that said "Are the videos from 2006 really helping?" My answer is yes, yes they are.

[@georgeedhan9224]

lel same

[@gabe5225]

its from 2008

[@slinkpot8798]

Ong

[@Retro3]

I’m getting that ad to this day lmao

[@dnick630]

right they say that like math ever changes

[@pepsico815]

Thank you for the videos. My professor assumes that everyone knows how to do this already, but the truth is that I forgot alot of this.

[@haileen6888]

You must be an adult now, wow! Now I'm suffering to learn this due to pandemic

[@silvo9460]

@@haileen6888 thats crazy time goes by so fast, now I am in the same postion as op, when he/she commented this I was 12

[@haileen6888]

@@silvo9460 really crazy ✨ hope you guys are doing well 🤍

[@MegaMed99]

@@haileen6888 y'all are beautiful humans

[@navanod001]

THE AMAZING THING ABOUT THIS WHOLE VIDEO IS THAT THIS IS THE SAME EXACT PROBLEM I'M WORKING ON RIGHT NOW! THANK YOU!!!!!!!! I ACTUALLY LOVE YOU RIGHT NOW!

[@patrickjmt]

i am happy that i was able to help you out on exactly what you needed! good luck on your midterm!

[@PBJJJ]

thank you!!

[@ShyDavis]

Taking calc now. Last math class was 4yrs ago. Some things were foreign. The professor did a very similar problem and I just couldn't figure out how he used the conjugate to solve. Then he gave us a similar problem for hw. THIS TRULY HELPED! Thanks so much!

[@misterkmo]

holy crap, you uploaded this 5 years ago, and it's still helping me out. Thank you so much, explaining step-by-step.....gaawwrd.

[@stayysid]

5 more years later, here I am .. P.S: It is STILL helping!!

[@samuelwalker9855]

Good thing math doesn't change much

[@RedApples16]

Such a life saver! I missed a calculus lecture today from being sick and looked up what was going on, Thank you so much! :)

[@Totsy30]

I know this video is 16 years old, but at 2:49 how does (x+2) -9 just suddenly become (x-7)??? Wouldn't order of operations require (x+2) to be evaluated before -9 could be applied?

[@angeltwotowns]

because uf you take out the parentheses, it would be x + 2 - 9 and subtract -9 and 2 so that becomes -7, the final would be x-7

[@yonati3590]

He subtract 9-2 which is 7

[@mypinkdollprincess]

You know what? I'm learning so much from and I feel really blessed. I just wanna thank you from the bottom of my heart! God Bless!

[@BB-li1wv]

You're basically my ap calc ab teacher, thank you for this!

[@patrickjmt]

Happy that I could help you!

[@squadbustersgamings]

+Brenda Benitez I thought this is Pre-Calculus topic?

[@BB-li1wv]

Jack Polo Uh no, not in my school or ap calc ab textbook

[@jlenangeleliang4525]

You should've gotten the parenthesis in the x+2-9 because you have already applied the foil method and so that the viewers wouldn't be confused. 😊🧡

[@angeloromulo123]

Actually got confused coz i thought the ones in the parenthesis are conjoined

[@jazzysmazzy3571]

i was confused about this thank you So much!!!!!!!

[@Totsy30]

Here I was so bewildered and confused thinking he ignored order of operations somehow. Seems it might've just been a writing typo

[@ibraham123]

Lol, this question is from "Calculus Early Transcendentals" Chapter 2.3. Man you're helping me pass 1st year calc with no background in it. Thanks a lot. 2 months ago I was sitting in the class like "wtf is a factor?" Great video, keep it up!

[@manicsurfing]

professors around the world are able to twiddle their thumbs while you do their work. thanks

[@BabyBeloooga]

On the verge of giving up on my studying and accepting defeat on the limits, I find these videos. THANK YOU!!!

[@patrickjmt]

@SavageInsight by definition, the square root of a positive number is a positive number.. so the square root of 25 is 5, and not also -5. HOWEVER, do not get this confused with solving an equation such as x^2 = 25. Then we do have to include both 5 and -5 as they are both solutions to the equation. also, graph y = squareroot(x) on your calculator. notice you only get the positive values!

[@1elitefighter]

great video! thanks, you really helped me a lot getting through trigonometry, now I'll definitely be looking at your calculus videos, keep up the good work!

[@user-tj5ex6md2t]

15 years later I see this and finally understand, thanks bro!!

[@sweetangel140]

thank you your videos on limits really helped me understand our professors last lecture which i was having trouble with :)

[@kris7695]

I was working a problem for 45 mins until I saw this video. Thank you!

[@patrickjmt]

@princetonjet glad u like it : )

[@seb090495]

I would die without you. I spend hours on your videos before calculus tests

[@TNCROCx]

you sir have aided me in means you will never know, yet i am eternally grateful. thank you

[@Tristan-M-1]

Thank you, you're helping me survive college Calculus all the way into 2023.

[@staind2523]

Excellent...a hard enough problem to answer my question and clear enough to not confuse me...thank you so much.

[@bezerk899]

Thanks Patrick. Your videos are truly a tool to succeed.

[@patrickjmt]

@saxyhank you are very welcome ; )

[@Foxyflexx44]

The part that you say its too much work to work ( denominator) thats the part i needed to see !!

[@DevinSmith1486]

thank you buddy i fell asleep in class everyday so this helps with my trig class

[@johnjlanejr]

THIS IS STILL HELPING ME! FYI

[@patrickjmt]

@I3lak happy to help, good luck!

[@ShinglongBok]

seriously i wish i had some spare change! these videos saved me from failing calc

[@rainbowandhardwork7901]

Thank you so much! This helped me understand the same type of problem I was a little confused on.

[@patrickjmt]

@pitmommy69 not sure what you mean... you for sure would not want to multiply out the denominator; if you do, you will not see that the (x - 7) ' s cancel.

[@GH123XL]

I could not agree with you more. This guy definitely needs to write his own book in calculus.

[@patrickjmt]

if you do not understand, just post a question here as a comment, and either me or someone else will usually get to it!

[@kennantunes]

damn this video’s over 10 years old but it’s still saving lives today 👏🏻

[@patrickjmt]

math doesn't change :)

[@larrydunaway2538]

Thank you for these tutorials...they help a great deal!

[@sunchoken]

beautifully done. incredibly simple and informative. great video.

[@patrickjmt]

@bobbyboy565 they cancel = they go away, which they do. that is all that people (myself included) mean. use whatever word you want!

[@patrickjmt]

@twobattaries ok. it kinda equals 52 as well then

[@jasminesingh246]

I honestly would've been screwed for my test tomorrow. Thank you for the video! greatly appreciated!

[@patrickjmt]

@karanaussie try the playlists, everything is organized.

[@nuhudabomb]

my god you are the best ive got an exam on friday ..all my lecturers are shit u are the best

[@VinnyGjokaj]

On all of his videos i get the advertisement for the "The tutor guy . com" and just think who would pay for his tutorials when we have the best tutorials from patrickJMT at a price all of us college kids can afford.. FREE.. Thanks for all your help!

[@stealthman612]

thank you so much this was an enormous help getting from point A to b, thank you!! =D

[@nutella871]

So glad these videos exist. Haha and relieved.

[@mastrammeena328]

0:33 what's radical in limit calculation???

[@azhandestructo]

thank you😭

[@alexandrac4582]

For the (x+2) - 9, I thought you couldn't touch the x+2 because the x and 2 are conjoined together by addition? But you just minused the 9 from it. Explanation please?

[@kurtbautista9158]

True i think the parenthesis is a further operation therefore its not supposed to be minused like that

[@joshua-jayechan5015]

he foil'ed, so i think that makes the parenthesis drop (which he didn't in this case) but then went to combining like numbers

[@patrickjmt]

@JMSCavaco the square root of nine does not also equal -3.

[@tigercece11]

THANK YOU SO MUCH FOR MAKING THIS VIDEO IT SAVED MY LIFE

[@kaciewassef2387]

Thank you this is so helpful

[@madinatouremedia]

thank you very much for this...this was a very detailed and clear explanation. this is something that my professor needs to start doing! =)

[@patrickjmt]

and for everyone 1 sarcastic comment, there are about 100 where i answer questions or am telling people ' work hard ' or ' thanks ' or whatever so let's keep it in perspective.

[@scarm095]

Thank you so so much! I am going to recommend you to all my friends.

[@KD-xx9su]

THIS VIDEO HELPED ME SO MUCH

[@AptFox]

Patrick I must say that you sir are by far my favorite human. You've made my college career so simple. I also visit patrick JMT (dot) com on a regular basis. Speaking of which, guys if you really wanna learn something head to his website as well as download one of his iPhone apps. I truly wish there were android equivalents, one of few things I'd gladly pay for.

[@microblan]

Thanks a lot, love these small videos, wish you had more examples though

[@patrickjmt]

@PIMPMASTATREX dont give up : ) Tons of calculus stuff here, so come back any time

[@krabbypatty3644]

please clear this up for me. when am i suppose to use this technique? is it only when there is a radical add/subtracted by a non radical? what about if its just a radical on the numerator do i multiply bit its conjugate as well?

[@Lllosiu99]

It doesn't reduce all of the radicals. Better way is to use the a^3-b^3 formula: a^3-b^3=(a-b)(a^2+a b+b^2), where a is a cube root of sth.

[@EVILICIOS]

THANK YOU GOOD SIR, GOD BLESS !! i think you might just saved me from failing my final !!

[@jasonsixtyone]

thank you so much!!!! helps me a bunch with my homework

[@bestsinger1289]

You are a kazzillion time better than my PROFESSOR in college!!!

[@patrickjmt]

glad you like them :)

[@uedikoz]

So, you've multiplied the original equation by 1 twice and still found the input 7 to give 0/0. It's a limit as x *approaches* 7, an easy quick check would be to input 6.99 into the equation, giving ~1/6.

[@mile8660]

You saved my life!!! Ackk, Thankyou!

[@ainsolehabintiabdullahmoe3138]

really helped me a lot. thank you so much

[@michaelpiotto4988]

if any one is interested in a different way to solve this (but its not necessarily easier) you can let u=(x+2)^0.5 thus x=u^(2)-2 and you factor, then switch back to x and solve for f(7). also the limit must change to be proper.

[@moisesserrano9888]

Better than my college calc professor 👌👌💯🔥

[@patrickjmt]

thanks lutetium for pointing this out... i sorta get tired of having to do it : )

[@jialechew4217]

how about if there is square roots in both numerator and denominator of the question? what should i do?

[@rpatiu]

Lerr Chew I have the same question, do you really multiply by the conjugate twice?

[@patrickjmt]

@Eureka3d i practice for one hour each day

[@1nglewattz1]

Fu222 yea! You totally simplified it using a graph chart. Thank you so, much.

[@RichEddie84]

At the risk of sounding too romantic. You are my life man!

[@mrtrcd123]

Thank you Patrick !!

[@princessindenial]

Thanks! this reaaally helped me.

[@WindBreaker77]

Does a function have a limit on every point of its domain as long as it's not an absolute value function or a piecewise function?? If not, how do you know whether or not you should check if the right hand limit equals the left hand limit?

[@Lllosiu99]

No, Sqrt(x+2) as a function has only non-negative values. Radical sign for real numbers means positive solution of x^2=a, even though this equation has two solutions for |a|>0.

[@Lllosiu99]

Yeah, but I'm talking about a^3 -b^3. If a is a cuberoot(x), then using a^2-b^2 formula you get just cuberoot(x)^2 -b^2, it doesn't reduce the cube root. If you multiply by a^2+ab+b^2, you get cuberoot(x)^3-b^3,which equals x-b^3, without cube root.

[@AnCa123789]

This is very helpful. Thank you very much!

[@brownnrl]

@bobbyboy565 Depends on terminology and popular expression. We use two different words "reduce" to represent inverse multiplication and "cancel" to represent inverse addition. However, almost all of my students associate "cancel" with "reduce". So I've replaced in day-to-day language "reduce" with "cancel" and "cancel" with "additive cancellation" to say which inverse operation is used. You should make a distinction between the two, because some students will confuse them.

[@patrickjmt]

no problem, come back any time!

[@JasonEkonomakos]

you write so nicely

[@thom8o]

This was the EXACT problem from my homework. What luck!

[@somyapatel3669]

Thank you sir .u made me understand limit concept

[@saxyhank]

That was so helpful thank you so much man! I had a really nasty lookin limit and I think il have an answer now! thanks dude!

[@maris6843]

Super well explained, thanks

[@patrickjmt]

Glad you liked it

[@patrickjmt]

@Mr4545723 glad they help

[@incletokrysmarlp.6244]

How did the numerator change?

[@uedikoz]

You only need to check that the limit is 7 from both sides if you're showing it's continuous at 7. For more complicated functions it may help you to experiment with different numbers, but in many cases like this you won't need to.

[@andrewsamir1361]

thank you man you saved my ass now i can study for the quiz XD

[@akvolkswagen]

This man is amazing!

[@yehlingboy]

thanks man.. now i can finish my homework

[@johncharles3907]

Very nice and clear. Thanks

[@bigmikec9]

Thanks. This really helped.

[@ohlyvya]

Thanks for the video, very helpful!

[@bilalabdurahman6875]

just wanted to thank you...i solved my problem!

[@hassan83111]

Hello, great vids mate. How would you solve ((radical 9x^2+x)-3x) i dont know if you get what the question is but the 9x^2+x is under the radical and then its -3x. limit x approaches infinity

[@hororian]

Tnx man, you saved my life.