Calculating a Limit at Infinity with a Radical

[leankints]

i have a test tom. my prof has been trying to teach me this for the past 3 weeks. i'm learning it in 9 min... i love you....

[MrDefeatist]

I'm assuming that if the highest powered x came with a number like 9x^2, I would divide all by 3x? or is it still just x?

[Vitdocet]

But for example: if i have sqrt{x^2 +3x}-x and i use your way i'll have:3/2x

 and it is 0...but real result is 3/2 or not?

[Vitdocet]

@Vitdocet sry solved...im stupid XD



[TifaChibiKun]

Your voice is beautiful! Thank you! This helped alot!

[KidKlassic91]

Thanks again ! But what about a problem with radicals up top ? I just raised the polynomial to 1/2 and continued as normal. Is that's okay ? Ex: Lim x--inf ( sqrt9x^6-x) / x^3+1 then becomes 9x^3-x^1/2 etc ...

[coldassassination]

What if you have for example 3x + radical(9x^2 +6x) do you multiply it by radical(1/x^2) but when multiplying by the 3x, we use 1/x? as in getting the radical 1/x^2 simplified?

[alamIbbar]

Thanks! You cleared up the negative-infinity problem for me.

[ThundaSundaa]

damn i wish you had a problem with a radical on top because i have no idea how to solve it :(

[patrickJMT]

@ThundaSundaa you do the exact same thing

[arielartista7]

Thank you. I'll make sure not to turn off my brain

[BritishTakeover]

I wish there were more teachers like you out there people where I'm from (NYC) pay $100s an hour for a teacher 1/3 of your quality!!!

[patrickJMT]

@BritishTakeover for a tutor maybe, but public teachers are not making anywhere near that

[MCNOVA21]

The only reason I am passing Calculus is because of these videos. Thanks for your help!

[patrickJMT]

@MCNOVA21 my pleasure : )

[chrisford619]

what if you have somthing like (sqrt(x^4+9))/(x^3+8) i worked it out to be -1/x^2. where do i go from here

[rwcarmody09]

Why is it 1 and not +,- 1 in the first example?

[GoooboopTT]

very helpful and effective. I think I should come your channel more often whenever there's an exam :P. Thanks

[patrickJMT]

@GoooboopTT come visit any time!

[dinotles]

wish I had something creative to say, you deserve something creative... GREAT JOB!!!

[patrickJMT]

@dinotles thanks : )

[CupppyCake77]

HALLELUIAH I NEEDED THIS!  THANKS FOR UPLOADING!!!!!

[tammibabs]

Thank you thank you thank you so much for these videos! Everything I didn't understand about limits last year in AP Calc now makes perfect sense to me. Wish I had discovered your videos sooner! <3

[7avidcyclist]

I watched the first example to find out how to do my assignment. I did all of the questions on it and then watched the rest of the video. turns out the second example was a question on my assignment and I had lost the negative sign in my work. thanks for the help!

[patrickJMT]

@7avidcyclist always happy to help a fellow cyclist ; )

[daesit]

wow your videos are 10^6 times better than my prof at mcgill

[lucuador1992]

This is really helping a lot! My calc professor is asian and he speaks with a THICK accent and because he is very experienced with this stuff, he tends to go quick when teaching us. So once I get left behind, I'm screwed! Thanks so much man!

[patrickJMT]

@lucuador1992 no problem, come visit any time !

[deadprisoner18]

@lucuador1992 is your professor xiawei wang by any chance? cuz thats the exact problem i have lol

[matserchaos1]

I had forgotten my password to my youtube account and used password recovery just so I can log into my account and comment on your video.

"I love you man, for real - no homo <3"

[patrickJMT]

@matserchaos1 : )

[admin8073]

you just saved me from losing silly marks on my calculus test. love ya.

[shelly2326]

So at the beginning of the semester I already had two F's and then I discovered your videos and so far I have gotten two A's!!! Thanks so much!!!!! :)

[patrickJMT]

@shelly2326 it is magic : )

[Kolbehh]

i fucking love this guy

[patrickJMT]

@Kolbehh normally i get rid of the comments with profanity, but i will leave this one : )

[DelGeeZee]

As X approaches neg infinity:

add the negative outside the square root of 1 over x^2 to preserve x going to negative infinity

Yahoo!!!!!!

[DelGeeZee]

@DelGeeZee only for odd powers

[HappyBokehs]

lol i know all this stuff and still failed math. holy crap

[anhhuyalex123]

thank you. you saved my life!

[bikeous23]

Isn't the square root of x^2 equivalent to the absolute value of x?? Or is that irrelevant in this case?

[nupsyyy]

can u help me with this problem:

lim under root(2x^2-3)-5x

x-->infinity

i know diffrentiaion but l hospital cannot be applied!

[Miss08Grace]

Your videos are more helpful than my lectures!! Thank-you so much for the examples!

[MsMakeupfreak1]

Hi. i have a quick question about the second example when x approaches negative infinity. Why do you not add the negative sign when you divide the numerator by the highest power 1/x?

[iagopb]

It's impossible that it always ends up right! I start then after like 2 pages of calculus I just find out that it's wrong.

[george241992]

Explain me something. There you have the same powers ( x^3/x^3) i know a rule that if we have the same powers the answer will be the coefficient of x^3/ the coefficinet of x^3/ so the answer should be 1.... could you explain. I'm sorry for my crrapy english.

[eellloashlayy]

Couldn't you have multiplied by the conjugate?

[206Nish]

Thanks for explaining the sqrt(a) * sqrt(b) = sqrt(ab). I knew that rule, but didn't know I needed to use it to divide the radical by x. Turning x into sqrt(1/x^2). Was always wondering where the x^2 was coming from.

[IMR707]

just 1 question of curiosity in 2nd question... is 1/x^3 at numerator doesn't need to put a negative on it?

[IMR707]

thnx... helps to ease my headache over this kind of question LOL....

[wullz16]

thx Pat :)

[lcdhdtv92]

do you always get the highest power from the denominator or from wherever the radical is preset? (Numerator or denominator)

[mustafamufasa]

@lcdhdtv92 you always get it from the bottom.

[Gr00veT00be]

i fucking love you man!

[theclack]

I don't think (Root (x^2)) = x. Does it not = the absolute value of x? Use x= -3 as an example.

[phuunggdiary]

would it be wrong if for the first example, i divide by x^2?

[Chynx123]

@phuunggdiary no ur right its just he demonstrated a different way

[Juanster23]

thank you thank you thank you thank you thank you thank you thank you thank you thank you.... and.... thank you!!!!

[coolguy4488]

I get some of this but not all...I havent taken any calculus classes and am very confused....As x approaches negative infinity?.....2 thing go wrong in my mind....I was told infinity was an adjective, not number. And therefore it cant be negative either. if something is infinite, shouldnt it be infinite going both ways not starting at zero?

[SirStrum]

Your videos are SO helpful! Please never stop making them. You have no idea how much these help; I've been going through examples we did in class, examples from the textbook, reading the textbook descriptions and it just gets more and more confusing. Thank you SO much for these videos!

[MusicBoxAnime]

hullo :)))))

can I ask.....what happens if the degree of the numerator is higher than the degree of the denominator?? my prof never explained about this..... :((

hope it doesn't come out in the exam. haha

[lawpetex]

Pardon me, doesn't sqrt(x^2) =|x| which turns into two values?

[RipplingSHockWave]

This is the only time I have felt the need to comment on youtube...Your videos are like hitting a calculus goldmine.

[patrickJMT]

@RipplingSHockWave but u have commented on a few vids already.... : )

[RipplingSHockWave]

@patrickJMT yes but if you check they are in the same day, so technically you're right, but you're videos are the only ones I have commented on haha, I didn't think anyone would look into it...

[wreynolds1995]

@patrickJMT not because he felt obliged to though, only because he wanted to

[Richux18]

@patrickJMT

what means his previous comments were probably smth useless ;d

[MsDolphin101]

@patrickJMT lmao!!!! omg i just wanted to tell you thank you for taking time out to do these videos. I swear i was failing this class an i'm determined to get an A. Thank yous soo much. Idk if u know how much it means to me, cause i suck @ math :(

[yortizful]

Can you explain some more exercises about the limit of an absolute value? Thank you so much for your help.

[GDrocks24]

my calc teacher is soooo baddd at teaching omg + boring (she is obssessed with cows too)..weird a sshit...dude all i gotta say is that you have taught me what she tried teaching me over like 3 months..thank you so much and keep up the good work man...so glad there are people like you who are willing to give time for others you freaking rock!

[russiawithlove101]

Thanks so much, I saw the negative sign used in my notes and didn't understand it, this helped me so much!

[halfcat7]

Fantastic video! Except, I'm a little confused at 5:37 when you found that the square root of 1/x^6 is the same as 1/x^3. Why is that? I would have thought it would be 1/x^9 because the square root of 9 is 3. Could you explain this please?

[unlacedandatrisk]

@halfcat7 Because when you multiply things with exponents, the exponents are added, not multiplied. (x^3)(x^3)=x^6

[bmx4637]

dude it is UNFATHOMABLE that 9 minutes of youtube beats an HOUR AND HALF of in class in my college. wtf, awesome.

[FeroxX]

dang, now i kinda get to know what is this dominator stuff. thanks!

[overdose312]

you're my new favorite person

[gladys0407]

thanks.. it helped me a lot... i just learn more when i'm listening at you.

[maslaczek1990]

But in this case x approaches to the infinity, so we can assume, that it's positive. If x would approach to minus infinity, sqr.rt of x would equal minus x (because sqr.rt is always positive)

[maslaczek1990]

square root of x to the second DOESN'T EQUAL x. It is equal modulus of x

[avionleahcim]

Thanks Patrick!

[saulhudson32]

pat your my hero

[izzasa666]

hey nice vid, u did not include any example with negative powers for infinite limits...e.g 3 power -x ...plz include one, will be grateful! thanku

[bbernens]

what if you have a radical in the numerator and the denominator?

[hasitha108]

why is it sqrt-1/x^6 and not sqrt-1/x^9?

[hasitha108]

@hasitha108 i got it...nvm

[pinkythongT]

I TOTALLY LOVE YOU

[petitange78]

If you had two tufts of white hair at the side of your head, and a ridiculously large tongue, people could seriously mistake you for Albert Einstein.

[patrickJMT]

@petitange78 i am getting quite a bit of gray hair. time marches on

[gulparo]

Gr8 Tutorial ...

[zombiecrowtv]

Thank you! My textbook sucks! It doesn't explain how to do this at all.

[213ciser]

how does one over the negative square root of one equall one

[bonkonthehead]

I L O V E YOU.

[butofcourse22]

thanks rey

[zabsem]

you are always the best. :)

[jdh428]

Thanks for breaking down limits with radicals..our calc professor didn't touch on this but assigned problems with it!

[psygoatrance89]

How do you tackle examples where u've got odd powers under the radical? Thx

[linkinms]

Users who clicked on (Dislike) are retarded!

[slartibartfast1992]

...or just use l'hopital's rule.

snide pedantic arrogance of mine aside, you rock! well explained.

[patrickJMT]

@slartibartfast1992 well, at the beginning of calculus, you do not even know about derivatives yet, so hard to justify the use of L'H : )

[ZanderTheLegendary]

@slartibartfast1992 hardly pedantic

[niggasinmaface]

shouldnt you use the limit laws before you skip all the way to the end?

[mypinkdollprincess]

oh You're making me fall in love with math all over again! Thanks a bunch!

[patrickJMT]

@mypinkdollprincess great!!

[mypinkdollprincess]

@patrickJMT OMG! I can't believe you replied to me! Thanks!

[patrickJMT]

@mypinkdollprincess lol - why cant you believe it? : )

[mypinkdollprincess]

@patrickJMT Cause, you're like a celebrity. I mean you'd be so busy with stuff. lol (:-

[patrickJMT]

@mypinkdollprincess celebrity! HAHAHAHHAHAHHAAHAH!!i am a very small fish in a very very small pond

[mypinkdollprincess]

@patrickJMT Well, that shows how humble you are(:- You're my role model and hero. Really, when I grow up I wanna be just like YOU! Go patrickJMT!

[patrickJMT]

@mypinkdollprincess aww : ) i am very flattered

[weezie1014]

I hate math, and you make it almost fun. almost. thank you for being so clear!

[patrickJMT]

@weezie1014 glad it helps : ) hopefully one day it will be just 'fun' instead of 'almost fun ' : )

[weezie1014]

I hate math, and you make it almost fun! almost. Thank you for making it so clear!

[goma14]

Thanks a lot!!!

[SONAL149]

hello sir. i m a gal belonging to india n must say that ur videos r a great help.

[valsera246]

Thank you! You just saved my life! Thank you!

[bl0rch]

Somebody give this guy an award, already. Patrick, you are the man!!!

[MrHoussy]

bra make your OWN website where we can watch ONLY your vidz coz they deep!!! luv em

[SydneyRover]

I am brushing up on all my calculus as I am intending to return to University and I must say that I find your videos really excellent. They compliment the material covered in the texts that I am using and improve my understanding in areas that I had previously found difficult. So I thank you indeed.!!

[alexfromcanada27]

THANK YOU from a fellow Austinite!

[missroxysurf]

What if the limit is not a quotient?

[77kooka]

Awesome! Thank you so much for making this understandable!!!!!!

[christinendanelian]

fancy

[mestisapnoi]

i love you. thank you so much for your help

[ArsenalRaffi]

Thank you!!! very helpful!

[IIIIISNEAKIIIII]

Thanks Patrick!

[ereke0099]

God bless you Patrick, you are helping many many students. keep doing it.

[DBYoshi685]

Thank you for showing ALL the steps.. Cleared a lot of "radical issues" up for me!

[AnglEys219]

Lifesaver...Thank you so much

[eldiosdedios]

Gracias, hombre.

[lexryuichi]

thx

[ali56]

does it have to be the highest power in the denominator or can it also be the highest power in the numerator if the thats where the highest power is

[renesisrx8]

yes, you choose the highest power in the denominator.

[ShortTheo]

yo man, i got 88% on my high school final, 95% on my 1st year university midterm cause of you! Final on monday, and i'm not too worried!

[ArickECA]

You are very generous. Thank you so much for all of your videos.

[Brendavarela]

I'm pretty sure you just helped me pass my calc final, aka saved my lifeee! Thank you so much.

[52689prettyflo]

hahah since i watch ur video i love DIF CAL now. rily big help to us tnx

[elbamb1n0]

just one word man Thanx u really a help on this i could get te handle of it now god bless ..=)

[TheExtremeCraziness]

i just love you

[hocuslocus]

Dude you are the best. thank you

[7777bambola]

thankkk youuu..ive been waiting to understand negative infinities for a longg timee..you are awsomee

[yoshi360360]

what happens if you got a odd power in the denominator?

[andreaseide]

thanks alot, i have been sitting for hours and days trying to figure out things for my self with my 1000 page math book and long boring lectures without any result, but your videos really helped me to finaly understand it =D

[Billmatica]

Thank you very much

[ysoni09]

Patrick Thanks for these videos man. I've been watching them for the last two years to help me understand my pre-calc and calc. thanks alot man

[SeminarClass]

you honestly do not know how much your videos have helped me. I was unable to understand ANYTHING my calc teacher talked about, but onw I see myself actually LIKING this math thank you you are truly my savior

[RunTooFree]

Nice video as usual, thanks.

How about some "Calculating a Limit at Infinity with Trig" and "Calculating a Limit at Infinity with Log or Ln"? Please!

[skyfaze]

very detailed and concise explanations.!!!!!

[ihatelucy11]

WOW. You just explained a few problems that I've been pulling hair out for almost 3 hours, in under 3 minutes. Possibly the only helpful calc vids I've seen yet!

THANK YOU for not repeating the same boring info over and over. So favorited.

[hollyxster]

Wow this really helped! I'm glad i came across this video =D

[andy120692]

very smart of you to catch that "-" sign at around 6:40

Will you be my personal teacher? haha

[utmicro31337]

awesome videos man! just started learning calculus this semester, and after watching ur vids i feel more confident about these problems!

[xsaburt]

I'm extremely afraid of my calculus test tomorrow, Since, we are focusing on hard limits, i'm really scared. But watching this vid, gave me some confident and new methods into attacking the problem. Please keep up the good work! :]

[khaled450]

man you rock ... I really like your videos. They realllly help me a lot. I can't thank you enough :D

[patrickJMT]

glad they help : )

[patrickJMT]

my pleasure!

and... you live in austin too?!

gooooooooooooooooo austin!! moved here two years ago and totally love it, although the heat is starting to make me go insane i think...

[libbeingcool]

this video saved my math life.

[iny0ureyes]

i wish you where my calculus teacher lol, instead of an 80 year old man who talks about theorems for 2 1/2 hours =/

[patrickJMT]

if you watch my videos, i am now one of your teachers at least : )

[MetallicaFTW7]

wait... on the first problem... why did you write 1/x on the second step? why didn't you divide it all by x? and i thought the square root of (x^2) is the absolute value of x?

so like okay your denominator of the first problem originally, square root of (x^2 + 4), would be divided by (x^2).... so that'd be (1/ + 4/(x^2)) ?

ugh im 14 doin summer calculus in 7 weeks.. and its confusing... id appreciate feedback asap since we have a chapt test on 7/8/09! thanks.

[taichikamiya]

Hi Patrick! :D Hey do u have any video about how to do trigonometric limits when the lim tends to some number but not 0?

[MetallicaFTW7]

yes i am having trouble on that too.... like lim as x approaches pi/4 of (cot^2 pi/4)/(sin pi/4)

do you have a video like that?

[ericasaidso]

I LOVE YOU!! *

* in a thanks-for-teaching-me-somethi­ng kind of way... sorry for being creepy

thanks again!

[patrickJMT]

u r not creepy : )

happy to help!

[dlittell]

when you're calculating a limit with a radical and X is approaching an integer would you still look for the highest power of X in the denominator, or would you use the conjugate method?

[dlittell]

I just saw another one of your videos and it answered my question. I'm taking calculus for MBA prep and even have a tutor, but you're much better than she is. Thank you! I'll be making a donation.

[rossicorona]

great stuff. this is so much nicer then re-reading my text book for the 100th time. i'll be making a donation for sure.

[sifl8898]

Does this work the same way with the radical in the numerator?

[unknownlove19]

for the second example

the limit sould be plus/minus 1, not negative 1

[patrickJMT]

how about : no way

[quareshmuah]

ya .... even i have been tought the same way. plus/minus 1 !!

[patrickJMT]

if that is what your teacher taught you, he/she was confused

[Suckthebeef]

Surely, if anything, it should be plus/minus 1 in both examples because it's the root of a positive number.

[patrickJMT]

surely, for sure, it should not be plus/minus 1.