Calculating a Limit by Multiplying by a Conjugate

[djtommytofficial]

Do you have any tutorials with limits that are containing: Pi, Third Root, Sin, Cos, Ln... ? Please help me i have exam in week i must graduate !

[prasiprassi]

tnx a lot i will sub all your vids i watch

[PIMPMASTATREX]

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

[patrickJMT]

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

[AnexFilms]

thanks a lot man

[some1unknown12]

omg! you are freakin amazing!

[Coheed275]

yes, the lightbulb. thank you!

[yehlingboy]

thanks man.. now i can finish my homework

[janialopez4242]

thanks you so much

[Speck174]

I love you!

[rajatsabharwal91]

dude you rock!

[karmaqueenn]

Saved my midterm! thank you so much (my teacher keeps writing "phrase" then writing "phrase2" saying its obvious how the connection is made. must watch more vids!

[18supercutie]

Thank you so much! This made conjugates so much more clear that i was able to finish my take home quiz.

[backsidethis]

Thank you for all your videos! An hour hour spent with your videos helped me understand things that my prof's spent weeks trying to explain.

[Eureka3d]

you can draw dotted lines really fast x)

[patrickJMT]

@Eureka3d i practice for one hour each day

[Jackiebug09]

couldnt the square root of nine also be -3, leaving you with zero and at square one?

[princessindenial]

Thanks! this reaaally helped me.

[karanaussie]

hey, i have to start with integration. i cant find the first basic video where you begin with integration. link please? thanks

[patrickJMT]

@karanaussie try the playlists, everything is organized.

[MegaSoulranger]

i love how you help, but its hard to watch at night, unfortuanatly most smart people i know, including you have a monotone voice, luls me to sleep :(

[assassin465]

Thank you this was helpful! But what if you just had radical x plus 2 in the numerater, without the negative 3? Would the conjugate just be radical x minus 2?

[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!

[patrickJMT]

@saxyhank you are very welcome ; )

[despicablerainier]

SALUT :))

[ohlyvya]

Thanks for the video, very helpful!

[puttputt1158]

You're awesome for this!!! :D

[angelofthestar]

u kno how much i love u???? u just saved my life today!!!! :) thanks!!!

[MrJasonekos]

you write so nicely

[JMSCavaco]

The square root of 9 equals +3, no doubt, but do it also equals -3. Do we just ignore -3 because it would later on lead to a non existent solution (something divided by 0)? Should we always check that?

Thank you very much, I'm watching you from across the Atlantic

[patrickJMT]

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

[twobattaries]

@patrickJMT ye it kinda does

[patrickJMT]

@twobattaries ok. it kinda equals 52 as well then

[SavageInsight]

@patrickJMT why isn't the square root of 9 equal to +/- 3?

[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!

[dookiekong007]

@patrickJMT He got burnedd, lol

[slashgashshorty]

@JMSCavaco lol im watching him from fucking abu dhabi :P

[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!

[vplof]

Hey please try this one limit when x tends to 16 of (4 - x^1/2)/(16x - x^2) couldnt make it

[majormuss]

I have a question- I thought the whole point of using conjugates in the first place is to get rid of it from the denominator.. how come you are using it to get it into the denominator again?

[RichEddie84]

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

[mlaldar]

Hey! You have no idea how much you have helped me tonight on my homework and even more . Thank you soo much!

[eexecutionstylee]

youtube math tutoring! love it. (:

[bobbyboy565]

This is really great, but one thing i noticed... you said the x-7s Cancel, well they don't. The actually reduce. A lot of people make this mistake, my self included. but really 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!

[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.

[stealthman612]

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

[nurpandbutch]

this is the exact problem i had to do!

[AnCa123789]

This is very helpful.

Thank you very much!

[microblan]

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

[LoveTogether27]

square root of t^2+16 X square root of t^2+16= t^2+16 right? or would it be t^4+16? i think its t^2+16 but my friend said its t^4+16.....i am confused.. someone help me?

[chibichibininjachibi]

What would you do if the bottom has a radical as well? (Squareroot of x - 7)

[mrwilliwizard]

oh man you make everything so easy! thanks!

[Mr4545723]

thanx mann 4 these videos,

they really helped me

cheers

[patrickJMT]

@Mr4545723 glad they help

[pitmommy69]

ok I got it now, I see that you leave it so you can cancell out :) Ok so if you wanted to work it out how would it go ?

[allude8]

thank you SO much!!!!!!!! this is much easier to follow than the examples in class!

[pitmommy69]

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

[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.

[nutella871]

So glad these videos exist. Haha and relieved.

[patrickJMT]

@nutella871 glad to ease your stress : )

[mchaos2010]

Thanks Veryyy much :D

[87loosegoose]

king among men...You helped me so much with my first course calc., this past semester, so many times. I've never been exposed to calc. before then and all this was new to me. Your the best.

[maybank1919]

I want to fire my non-english speaking math prof. Thank you!

[nigahdik]

Dear PatrickJMT first of all thanks for yours kind help 2nd upload yours videos by proper order such as What is Limit?-01 etc. Thanks again

[hororian]

Tnx man, you saved my life.

[intelligentwhirl]

YOU ARE AMAZING!

[fredlove0500]

you are awesome!!

[dxb6636]

Patrick your the best ,, I got A+ in Calculus because of your amazing videos ,, Keep it up bro wish u all best =)

[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!

[SuperWolfpack17]

You confused me at the part wher (x-2)-9 turned out to be x-7...at that point i would have just plugged in 7 and assumed the limit was going to 0 but i guess the paranthesis just confused me....otherwise this video is FANTASTIC!!!

[nuhudabomb]

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

[xcvsdfwer234]

I love how "cancel" means: add to get zero, divide to get 1, and even a square 'cancels' a square root!

[minerva1115]

I was just looking for a quick review before my math test. Your videos are a phenomenal help and I am now thoroughly prepared! Thank you!

[deathshot7]

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

[reighteeen]

this will help me on my ap exam tomorrow..

[patrickJMT]

@princetonjet glad u like it : )

[Sinead445465]

wow im in love!

[patrickJMT]

@Sinead445465 ha!!

[kumarimay]

you. are. incredible. I sincerely thank you, for you have made my life worth living :)

[Knarkill000]

Yeah it's simple algebra, what of it?

[krs126]

what if X+7? I know if its a minus sign at the bottom, mulituply it w/ a plus sign. Then what if a plus sign? switch to a minus?

[gundam2388]

How come you dont have to distribute the top (x+2)-9?? wouldn't that give us 9x-18?

Because I always thought when their are parenthesis you have to distribute to get rid of the parenthesis. Anyways still a very usefull vid though, I am having my calculus exam in 2hours and 45 min. Thanks to your vids I know that I will pass them :)

[stadnek]

at 2:30 would the -9 have not been distributed to the x and the +2, giving: (9x-18)???

[Humbleone123]

The 9 is subtracted, not multiplied. If it were -9(x+2) it would have been as you said.

[aeropostale]

what happens if there isnt something to cancel like the seven?

[mraberrant]

you just saved my life you lovable bastard

[brent0007]

this guy is the only online video tutor ive seen that has made sence to me. All of his videos make things so much easier to understand

[karlkarlkarl1234]

conjugates!?!?

[TheCzechMisha]

I love you! :)

[amaka56]

wow, all his vids are amazing

hey guys, if you're well off do us all a favor and donate to this guy

seriously, he deserves it

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[ShinglongBok]

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

[alexgordonepic]

Toda Patrick!

[aznboi1214]

AWESOME! great teacher

[guyinbike]

just put 7.001 if x approaches to 7

[kickit246]

thanks dude i got a calc midterm in 2 hours lol :D

[baseballman94]

my teachers is a bitch and has tried teaching us this for 2 weeks no one gets it. i am the only one in class that gets it and poeple dont believe me when i tell them i leanred it all off youtube! i dont even bother paying attention in class anymore i just learn it when i get home.

[hghar33b]

Thank you so much!

I've been having such a hard time trying to understand this.

Thanks again. :]

[degrassicutie1]

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

[dannyodandan]

ur sqr roots are sexy :D

[staind2523]

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

[smilewolf99]

that's helpful and clear, you are gooooood.

[bestsinger1289]

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

[thom8o]

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

[maskedlove29]

haha, same I got this as one of my questions :P and I just happen to have problems with this one :)

[misterguth]

yeh that's because most teachers probably learn from youtube the night before they have to do something as well =D

[julub]

that was helpful

[fouraid57]

Isn't the answer 1/6 if x isn't 7 ? because of the simplifying ..

[amcbirds]

man why don't u come to houston and do ur tutoring instead of in austin???

[mrghettobiscuit]

I got the limit does not exist. You are wrong because i checked on my graphing calculator after evaluating the limit and it confirmed by work. After multiplying the top and bottom by the conjugate of the numerator, you are supposed to then times the numerator and denominator by 1/abs(x). Then you input 7 into each part, where applicable, and everything cancels, leaving you with 0/0, or does not exist.

[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.

[cooleoe]

my teacher said you can't do that. This girl tried that and he shut her down lol. He said you have to have a list of functions showing that the limit is heading to that number, because the next number might not be the same. So like you'd have to put 6.9, 6.99, 6.999, 7.001, 7.01, 7.1 into the function to make sure that from both sides the limit is really heading to 7. That would be a numerical way, but this guy solved it algebraicaly.

[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.

[mrghettobiscuit]

Whoops, I apologize. I wrote the problem incorrectly and ended up with a completely different answer. Your original answer of 1/6 was indeed correct. Anyways, great videos! Keep up the good work.

[taichikamiya]

How can I do the conjugate when its a cubic root??? I cant do it :(

[aparrotslife]

I like your helpful videos.  Thank you. :)

[1nglewattz1]

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

[Yu2Kal]

At 3:47 the square root of 9 could also be -3, -3+3 = 0?

[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.

[gagoboy08]

hey thanks! Godbless!

[Reeko599]

alright how does (x-2)+9 go to x-7?

[lukasgomes1428]

lmfao dude first of all its x+2-9....it becomes like 2-9 which equals -7....

[Reeko599]

(x+2)-9 is different from x+2-9...

[lukasgomes1428]

yea but the answers are the same...

[Reeko599]

im pretty sure (x+2)-9 equals -9x-18 but i might just be retarded. i don't care anymore i already took my final haha. and if i have been wrong this whole time here's some surprising news. I'm actually in advanced math lol

[RunTooFree]

(x+2) - (9) ≠ (x+2) x (9)

[Yu2Kal]

Yea they are different, however they still both give the same answer for any value of x.

[kasper9016]

Use L'Hopitals rule u can get the same answer and it is faster, nice video anyway

[lutetium1907]

true but this is not the point of his video

[patrickJMT]

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

[shellyshakeup]

you are absolutely amazing! thank you!

[safiullahsss]

plz post some new vide on limits

dude u did a great job

[neves783]

Good thing I found this video. By the way, I also encountered those radicals in one problem. The only thing that bugs me, though, is that the radical is a cube root and not a square root, so I just want to ask what the conjugate of a cube root is. Thanks again.

[neves783]

thanks! :)

[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.

[PandaBear2910]

What do you mean?

a^2 - b^2 factors into (a + b)(a - b). You can foil it to see.

a is the cuberoot(x) and b is more adding on to it.

[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.

[turbobeefmkiii]

Ultimate service. Much appreciated; 5 stars!

[davidenelson]

5 stars man.

Seriously, thanks

[mzhappy516]

omg you helped me soo much i give you so much thanks

[dorothydorothy111]

thanks again...i think i am going to make a pot of coffee and watch all your videos tonight hahahaa ;-P

[sokkakings]

i know right

[maruahmed]

thank you

[bebenader]

WOW your pretty darn smart. Thanks for the help =)

[ohmannhey]

Very good ... greetings from Germany ... very helpful .. Thanks.

[aboudzidane105]

Thanks a lot for the video.

[mawgwd]

thank you so much

[ViadoMundo]

Thanks!

[majesty030]

when you got (x+2)-9, why was the result -9, instead of -9x-18.

[mawgwd]

he takes -9 as common to simplify the equation

[alisma12]

why was a 1 left on the top??

[patrickJMT]

well, imagine simplifying 2/2... after you cancel out the two's, are you left with 0?

[shafenator]

thank you very much. I am studying for my calculus I midterm next week, was getting stuck on the radical problems. and it was this exact problem i was doing from my book that you did. you helped a ton, thanks

[patrickJMT]

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

[wing43]

thanks a bunch. i think i got the idea

[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!