Thanks for all the info. Your tank work video has helped me study for my final, the most. I've been a bit iffy on the work problems, before. /Really iffy. >>'
This is negative one raised to the n-1 and all of that divided by 2raised to the n power. Can i use the Root Test for that or should i used the alternating series test better? Is it incorrect if if i use the root test for this?
I think the second example has a small error. The denominator has the (3^3)(3^1/n). You say that this becomes 27 as n goes to infinity. I'm pretty sure that it becomes (9)(1) not (9)(3) since 3^0 is 1 not 3. Doesn't matter because the numerator is infinity, but still a comment is warranted.
@js6781535 No, it looks like it will at first glance but the number that is being raised to the n'th power is approaching 1 as n goes to infinity. ie - (1+Very Small Number)^(Very Large Number). As he points out, this is the definition of the number e or approximately 2.718 ...or 2.7 1828 1828 45 90 45 (broken up into the memorization pattern to the 16th significant figure, like anyone would ever do that)... Still absolutely convergent either way, but 1/e was correct.
God bless you dude! You have no idea how much these videos have helped me for my cal 2 final. the limit of my appreciation for your work approaches infinity. Great work!
Here is what I have gotten: The sum of (n^n)/(3^(1+3*n))= the sum of (n^n)/(3*3^(3*n)) which could be looked upon as (1/3)* the sum of (n^n)/(3^(3*n)) which could also = (1/3)* the sum of (n^n)/((3^3)^n) = (1/3) * the sum of (n/27)^n which if you then apply the root test and and take the limit of this sum, you would have (1/3)* the limit as n->+infin. of [(n/27)^n]^(1/n)= 1/3 * lim. as n-> +infin. n/27= 1/81 * lim n-> +infin. of n. If you then apply l'Hopital's rule, you reach a limit of 1/81.
Thank you very much for the videos. i use them a lot!! i always stay up all night every thursday to study for my weekly test on friday and without these videos i would not be doing as well in my calc 1 class last semester or my calc 2 class this semester.
Near the end of the video, you said "Well, 1 to the n is just 1", but we are taking the limit when n approaches infinity. Isn't 1 to the infinity an indeterminate form?
sorry, but why did you multiply top and bottom by 1/n? i was doing your problem and i felt legit because i was following the right steps, but instead of multiplying top and bottom by 1/n, i just distributed the n power and got 1 as my limit :(
@patrickJMT i mentioned the same thing on one of your other videos also, i think the reason why people think it is boring in a classroom is because computer are just fun, or some kind of drug that emits out of our computers, lol
@patrickJMT No, it's different. Watch Salman Khan's video on Ted. There's a huge difference between listening to someone talk to you and then expect you to understand, vs being pre-recorded so you can stop, pause rewind or choose another person to listen to. We teach math like it's 1799 in this country, and it's friggin retarded.
dude i haven't even reached at this level of math yet , and im just sitting here and watching it....idky but who knows maybe it will help me out in the future
You are awesome. But aside from your teachings, I like your voice, the fact that you're left handed, and that you love Math as well. But now it's time for Diff Eq.. I must leave you.. Thank you for the videos to brush up on my series!
thank you so much for being there i have been watching you videos for the whole day today about this topic..........they are very much easy to understand..thank you again!!
@patrickJMT i like it when you go into the conceptual depths but at the same time keeping maths enjoyable, i feel really grateful to you., you just inspire me.....i like "improper integrals" in your video series very much :-)
thank you so much for being there i have been watching you videos for the whole day today about this topic..........they are very much easy to understand..thank you again!!
these videos are very much helpful i have been watching sequence and series topic for almost 8 hrs with small intervals and practicing problems in between ....i hope i will do well in exams
thank you so much ....people like you should always be there ....!!
Brilliant stuff. As an aspiring physicist at the university of Oslo, in Norway, these videos have given me a much needed pre-exam repetition. Keep up your excellent work.
Hey man you`re so great ......I doubt if you`ve ever heared of Jordan in the middle east ....but you know,you`ve helped me and bunch of my friends with our calculus I&II here in Jordan so keep up the great work &
@patrickJMT Actually Jordan is a place in the Middle East. FYI: "The small Kingdom of Jordan occupies a strategic location in the Middle East. This arid and ancient land (of biblical fame) has witnessed centuries of conquests and invading armies. " Search More On Google if interested :)
i would just like to thank you. you have no idea how much you have helped me. thank you so much i really appreciate it. if only all calculus profs were like you.
thanks alot for the videos. i just wanna know what kind of whiteboard or white sheet of papers you writng those things on? i like it i wanna know the name so i can get it for myself. does anybody know the answer? help pls!
Well you probably get bored of hearing it, but you've saved yet another student. Thanks for these videos. You're doing something great for students everywhere.
Patrick how do you do it? I wanted to make some Linear Algebra vids but my voice became shaky, lips and tongue became stiff, nose started spasming (like stage fright), needless to say I didn't post those videos. How on earth do you keep your voice so calm?
i figured that if they suck, i would just delete them. most people seem to like them though : )
and honestly, i forget half of this stuff, so i make them for 'future me' - the one that has forgotten and re-watches old me (newer me?), so i have to be nice and soothing to my future self : )
"most people seem to like them though" No No Patrick. Everybody LOVES them. You are a great man. Thousands of students around the world are more grateful than you know. Thank you for the time and effort you put into these videos. They have saved the lives of many students.
For the last example on this video it is easier to use L'Hopitals on that limit by taking the ln of the limit instead of having to memorize that that limit equals e. You can show why it equals e.
Patrick. If I ever see you, I will kiss u on the mouth. This stuff is absolute greek and then you come in and put it all in layman's terms and voila, it's like magic. My brain has been having the "AHA" moment all day. Thank you sooooo very much dude. You make me wanna bake you cookies. That's saying something.
So basically, series with (a sub n)^n, you can treat "a sub n" as your common ratio (r), and your (a) as 1 so, if r < 1, then it's convergent. Just right out of your first couple of videos.
OMG I agree with Inferfire........it is plain scary that I understand all your root test/ratio test stuff, I have my final tomorrow and before these videos I thought I was screwed because i have absolutely NO idea what my prof is babbling about....I wanna seriously thank you so much!!!
what do you call when you multiply num and denom by 1/n, and one more thing patrick... why the denom ...(1+1/n)^n equals e?... it shouldnt be 1? thank you in advance
(1+1/n)^n Is a notable limit witch equals e, look for it... and the 1/n multiply by num and denom is just a simplification, it doesn't affect the equation as you are using it in the top and the bottom..
i have a question on the second problem when u got to lim of (n/n+1)^n..isnt that e..y did u do all that other stuff like mult top and bottem by 1/x to get the 1/e?
Great videos, they are really helping my preps for the exams! By the way, at 5.45 you say that 0*27=27, not that it matters, the answer will still be the same.
well, it is basically knowing that the n/(n+1) is the flip of (n+1)/n; that raised to a power of n has something to do with 'e'! i am seen that limit so many times now, that i just recognize it. so to answer your question, what made me think to do that is: experience!
sometimes one has to be shown what to do a few times before it sticks!
the problem is if you have a function of the form [f(x)]^[g(x)] and f(x) is APPROACHING 1 (but not necessarily equal to 1).
limit notation is not very good; the standard notation is to use equality, when in reality it is just 'getting close' to that number (in most cases). eventually, one figures this out and just learns to deal with it : )
Great video! I have a test on Tuesday and your videos have been so helpful.
I'd just like to let you know, though, that this video's not on your website.
Thanks again!
BreakneckWalrus 2 weeks ago
@burnskate2
3^-n = 1/3^n. As n approaches infinity the denominator gets bigger therefore limit = zero
richak7 1 month ago
Thank you for your videos! Everything is so clear.
MK472009 1 month ago
Erm.
@ 5:27
.... Doesn't 3^(-n) approach 1, not zero?
Otherwise it would be infinity/0...?
SIDENOTE:
Thanks for all the info. Your tank work video has helped me study for my final, the most. I've been a bit iffy on the work problems, before. /Really iffy. >>'
burnskate2 1 month ago
i love you! thank you so much. ive been watching your videos all day for my final tomorrow. i think ill pass it because of you! :)
gr3engirl 1 month ago
I LOVE YOUR TUTORIALS!!!! THANK YOU. I'M SO GONNA ACE MY CAL TEST!!!!!! :DDDDDD
ceny021 1 month ago
We left-handed humans are far superior in mathematics and physics...
990032shizzam 1 month ago
just started studying this in calc II and your video was very helpful. sound quality was good and you made this topic less frightening!
FlakeyOkie64 1 month ago
patrick you rock man
h0s3a 1 month ago
Question:
If i have an alternating series [(-1)^n-1]/2^n
This is negative one raised to the n-1 and all of that divided by 2raised to the n power. Can i use the Root Test for that or should i used the alternating series test better? Is it incorrect if if i use the root test for this?
mariosmustache 2 months ago
@engineerrob 3^3 is equal to 27
chevyboyz01 2 months ago
Wow! incredible... especially the very last part of the root test!
MrMankoe 2 months ago
You're my favorite teacher! =D
NgJackal1990 2 months ago
I think the second example has a small error. The denominator has the (3^3)(3^1/n). You say that this becomes 27 as n goes to infinity. I'm pretty sure that it becomes (9)(1) not (9)(3) since 3^0 is 1 not 3. Doesn't matter because the numerator is infinity, but still a comment is warranted.
engineerrob1 2 months ago
wouldn't the limit for the last one be 1/infinity? which is equal to 0 and its going to give you absolute convergent
js6781535 2 months ago
@js6781535 No, it looks like it will at first glance but the number that is being raised to the n'th power is approaching 1 as n goes to infinity. ie - (1+Very Small Number)^(Very Large Number). As he points out, this is the definition of the number e or approximately 2.718 ...or 2.7 1828 1828 45 90 45 (broken up into the memorization pattern to the 16th significant figure, like anyone would ever do that)... Still absolutely convergent either way, but 1/e was correct.
engineerrob1 2 months ago
you are my new God!!!!!!
unknownshadow892 3 months ago
good for the soul =)
randookie3 3 months ago
You sir are an angel sent from heaven above. this is a legitamate lifesaver.
RaChElSfRoGs12 3 months ago
Dude I think I love you :D
casperv7 5 months ago
Great lesson!
VinzVT 5 months ago
You're a life saver
Tbrown922 6 months ago
@yasthilmaharaj is right. Me and my friends from different colleges all use you to get througth calculus classes. Its great
blinkdrumr16 6 months ago
This has been flagged as spam show
I FUCKING LOVE YOU!!!!!!
lobsidedballs 7 months ago
God bless you dude! You have no idea how much these videos have helped me for my cal 2 final. the limit of my appreciation for your work approaches infinity. Great work!
rahlity 8 months ago 40
This has been flagged as spam show
Get a good friendship with good girls naneedj.info
darshi48 8 months ago
4 people are teachers who suck at teaching and force students like us to youtube calc lessons -__- BTW, huzzah to my AP warriors out there!
rhythmsurf3r 9 months ago
Thank you!
1ordofsarcasm 9 months ago
Thank you so much! My calculus teacher put a question in our test that used the (1+1/n) limit for e as a sort of "trick" question.
countingxchameleons 9 months ago
Am I just completely off, or is it plausible ? Thanks, and please point out any errors if so.
07ziul 9 months ago
Here is what I have gotten: The sum of (n^n)/(3^(1+3*n))= the sum of (n^n)/(3*3^(3*n)) which could be looked upon as (1/3)* the sum of (n^n)/(3^(3*n)) which could also = (1/3)* the sum of (n^n)/((3^3)^n) = (1/3) * the sum of (n/27)^n which if you then apply the root test and and take the limit of this sum, you would have (1/3)* the limit as n->+infin. of [(n/27)^n]^(1/n)= 1/3 * lim. as n-> +infin. n/27= 1/81 * lim n-> +infin. of n. If you then apply l'Hopital's rule, you reach a limit of 1/81.
07ziul 9 months ago
just so you know your the man. . .helped me through my calc II class with relative ease. Best vids on the net for sure.
shanus180 9 months ago
Lefty flip forever
notenufpowerinthis 9 months ago
How many people just noticed he was left handed when reading this comment?
graisonf 9 months ago
sergio sanchez can die for all i care
Saladin15 9 months ago
i love you.
spicyxlilxman 9 months ago
Thank you very much for the videos. i use them a lot!! i always stay up all night every thursday to study for my weekly test on friday and without these videos i would not be doing as well in my calc 1 class last semester or my calc 2 class this semester.
tjdudeman 10 months ago
Thank you so much for making this easy to understand! Fantastic.
emjab68 10 months ago
Near the end of the video, you said "Well, 1 to the n is just 1", but we are taking the limit when n approaches infinity. Isn't 1 to the infinity an indeterminate form?
EffingNinjasFTW 10 months ago
thanks man...
kerryben40 10 months ago
sorry, but why did you multiply top and bottom by 1/n? i was doing your problem and i felt legit because i was following the right steps, but instead of multiplying top and bottom by 1/n, i just distributed the n power and got 1 as my limit :(
care to explain that 1/n thing?
hothotcow 10 months ago
I started writing my root symbols like yours. :)
blkfsty555 10 months ago
very clear explanations !!! I FINALLY GOT THIS!! thank u. I am really appreciated.!!
canopppppyyyy 10 months ago
You rock, man. Better teacher than my Calculus professor. And I go to a major university too! =O
armidylano44 11 months ago
@armidylano44 well, i used to bore people at a major university as well, so maybe it is all the same
patrickJMT 11 months ago
@patrickJMT
Hey, I noticed you're from Austin. I'm actually at UT right now =)
Anyway, thanks again. King of youtube math, you are.
armidylano44 11 months ago
@armidylano44 ha - give me a big high five if you see me on campus or at cafe medici later!
patrickJMT 11 months ago
@patrickJMT ur a TA?
remirap 11 months ago
@remirap no, i am long done with school.
patrickJMT 11 months ago
@patrickJMT i mentioned the same thing on one of your other videos also, i think the reason why people think it is boring in a classroom is because computer are just fun, or some kind of drug that emits out of our computers, lol
jiamonx2 9 months ago
@patrickJMT No, it's different. Watch Salman Khan's video on Ted. There's a huge difference between listening to someone talk to you and then expect you to understand, vs being pre-recorded so you can stop, pause rewind or choose another person to listen to. We teach math like it's 1799 in this country, and it's friggin retarded.
Raxarax 9 months ago
@Raxarax i was being a bit ' tongue in cheek ' with that comment
patrickJMT 9 months ago
@patrickJMT Ya, I know, but I wanted to vent to someone...
Raxarax 9 months ago
dude i haven't even reached at this level of math yet , and im just sitting here and watching it....idky but who knows maybe it will help me out in the future
flawns 11 months ago
at 6 minutes, isn't it supposed to be 0 times 27? why does the bottom equal to 27? Shouldn't it be infinity over zero? Sorry, confused!
christalwang 1 year ago
@christalwang it's 3^0, not 0. 3^0 equals 1, so the 1x27 = 27
robert19w 10 months ago 2
@christalwang i was wondering the same thing... i am now scrolling through pages of comments to see if this was addressed..
shortyife 2 months ago
You are awesome. But aside from your teachings, I like your voice, the fact that you're left handed, and that you love Math as well. But now it's time for Diff Eq.. I must leave you.. Thank you for the videos to brush up on my series!
BlueColourPencils 1 year ago
@BlueColourPencils awww, thanks! go texas!
patrickJMT 1 year ago
thank you so much for being there i have been watching you videos for the whole day today about this topic..........they are very much easy to understand..thank you again!!
vjbhatt96 1 year ago
@vjbhatt96 i hope i have not bored you to death yet ; )
patrickJMT 1 year ago
@patrickJMT No not at all. Your vids just drive me crazy to learn maths whole day long!
vjbhatt96 1 year ago
@vjbhatt96 ha, i find that amazing : )
patrickJMT 1 year ago
@patrickJMT i like it when you go into the conceptual depths but at the same time keeping maths enjoyable, i feel really grateful to you., you just inspire me.....i like "improper integrals" in your video series very much :-)
vjbhatt96 1 year ago
thank you so much for being there i have been watching you videos for the whole day today about this topic..........they are very much easy to understand..thank you again!!
vjbhatt96 1 year ago
these videos are very much helpful i have been watching sequence and series topic for almost 8 hrs with small intervals and practicing problems in between ....i hope i will do well in exams
thank you so much ....people like you should always be there ....!!
vjbhatt96 1 year ago
you need to learn how to write a sigma lol!
joejacksonriley 1 year ago
Thank you very much for your sharing ~ !!
samson2088 1 year ago
5:48 infinity/0 not infinity/27
thekillerz12345 1 year ago
Your videos are very helpful. You are very clear and give helpful tips. Thank you very much!
sainthestreets 1 year ago
why is is 1\e as n goes to infinity why u dont make it one and anypower to 1 is 1...
jasskarn666 1 year ago
how can i succed to all my future math courses as u said do we have to hard working or we have to born with a math worm.....
jasskarn666 1 year ago
At 5:39, doesn't the plug and chug just give infinity/0, not infinity/27? But infinity/0 is not indeterminate anyway, so it doesn't matter?
archiemedes42 1 year ago
swear to God man, if I ever get a degree and a decent job, I am making a LARGE contribution to your cause! THANK YOU!
mpatt79 1 year ago
I noticed you bend the cap on your marker, haha I do that too!
TheSwagerking9018 1 year ago 9
Thank you so much Patrick!! You are truly a noble man. Wish i would do more than jst saying thank you....
God bless yea.
denokindo 1 year ago
What video do you show the proof of the limit (1+(1/n))^n = e?
resevil787 1 year ago
You are a great help, Patric! :D
Nazmus1992 1 year ago
If 1/n -->0 as n -->infinite, why does it matter what An is if anything to the power 0 is 1?
tbone76749 1 year ago
why didn't they teach this in alg 2/college algebra? it would save me all that studying for calc ii.
occocooccoco 1 year ago
@patrickJMT in example 3, why did u multiply numerator and denominator by 1/n in the second or third step of the problem?
swativ7 1 year ago
@patrickJMT
Thanks for all your videos!! Its much easier for me to study math when I can pause and rewind the lecture :)
But I have a question, say I have a sum of (x/n)^n
what do I do with x?
at the end I got:
lim (x/n)
do I say that it converges for x<n? I coulndn't find examples in the video where there was x as well as n
maethorlotr 1 year ago
omg, thanks a ton patrick!! i have a maths exam next week, luv ur videos so much
heytarotpipi 1 year ago
You've got a flair for teaching, man! Try getting on a seminar circuit. Do you have your Masters?
BornAtTheBar 1 year ago
@BornAtTheBar yep, got a masters
patrickJMT 1 year ago
wow i feel dumb lol
erick1076 1 year ago
Dude you are the best man. I appreciate the time and effort you put into your videos.
dportal2006 1 year ago
Brilliant stuff. As an aspiring physicist at the university of Oslo, in Norway, these videos have given me a much needed pre-exam repetition. Keep up your excellent work.
88Revanius 1 year ago
Hey man you`re so great ......I doubt if you`ve ever heared of Jordan in the middle east ....but you know,you`ve helped me and bunch of my friends with our calculus I&II here in Jordan so keep up the great work &
God bless You:D
5ANASHEEROA 1 year ago
@5ANASHEEROA do you mean michael jordan? was he in the middle east?
patrickJMT 1 year ago 8
@patrickJMT eeeeehhh, Jordan is a place >>
corpsemunger 1 year ago
@corpsemunger pretty sure it was a joke man
SeraphInvictus 1 year ago
@corpsemunger yes......i live in west jordan utah
Amaoricans 1 year ago
@patrickJMT lol... I love your sense of humor
SeraphInvictus 1 year ago
@patrickJMT lol
shasanni 1 year ago
@patrickJMT Actually Jordan is a place in the Middle East. FYI: "The small Kingdom of Jordan occupies a strategic location in the Middle East. This arid and ancient land (of biblical fame) has witnessed centuries of conquests and invading armies. " Search More On Google if interested :)
avik58 1 year ago
@avik58 pretty sure it was sarcasm man.
ichinarukurumaki 1 year ago
@patrickJMT no theres a place called jordan located in the middle east. You are making such a huge a positive feedback
beansombrero 1 year ago
@beansombrero lol patrick was just kidding...
teeheetiti 1 year ago
@patrickJMT Lol.idk if that was a joke. But he meant the country Jordan.
msingh32 1 year ago
Thank you very much, all these videos Make my life so easy!
Millenx 1 year ago
bro, thanks a lot for your videos.
i'm a math tutor in my spare time, and i very much respect your concise and confident teaching methods.
this series of videos helped me refresh on power series for my (ultra-brutal) complex analysis class!
franciswusher 1 year ago
couldn't focus on studying, kept watching youtube videos, now I have found the perfect combination. Youtube+studying=progress
CinaedFLM 1 year ago
Geez you make it much easier to understand than my professor...great stuff!!
ThangkhungNay 1 year ago
Fantastic!!!
HoloUniverse 1 year ago
i would just like to thank you. you have no idea how much you have helped me. thank you so much i really appreciate it. if only all calculus profs were like you.
jabrakadio 1 year ago
YOU ROCK. I have a calc test this upcoming monday
omnifur 1 year ago
why at the end of the second example does the last step he got: inf/(0X27) and he said it turns into =inf??
Isn't this incorrect?
I solved the problem by taking the third from the series itself and then you won't get that 0 at the bottom.
can n e one clarify?
showABCshow 1 year ago 2
@showABCshow he did it right. anything over infinity is zero, therefore one over infinity is zero therefor 3 ^ 0 = 1 so the denom is equal to 27
spacebird413 1 year ago
@spacebird413
wow.. my bad I just saw that 0 there and I thought he meant 3^(1/n)= 0, but he meant 3^0.
Thanks.
showABCshow 1 year ago
Awesome video dude, this helped me a ton thank you
tjwick63 2 years ago 4
5 star
al7rbi1981 2 years ago 2
definitely wish u were my calc teacher instead of the ones i have -they all suck
balla4life123 2 years ago 3
you are amazing
frenchpandas 2 years ago 5
Very helpful. Much better than my cal II teacher who assumes we know everything.
vdubnthehouse 2 years ago 42
@vdubnthehouse seriously -.-
MuseICxfuhnatic 1 year ago
thanks alot for the videos. i just wanna know what kind of whiteboard or white sheet of papers you writng those things on? i like it i wanna know the name so i can get it for myself. does anybody know the answer? help pls!
phakoko 2 years ago 3
the name of what he is using is called printer paper and permanent markers.....
mintyman89 2 years ago 7
Well you probably get bored of hearing it, but you've saved yet another student. Thanks for these videos. You're doing something great for students everywhere.
aroguegurklis 2 years ago 5
thanks man, you absolutely rock!!!!
stanke89 2 years ago 5
Patrick how do you do it? I wanted to make some Linear Algebra vids but my voice became shaky, lips and tongue became stiff, nose started spasming (like stage fright), needless to say I didn't post those videos. How on earth do you keep your voice so calm?
Nanumir 2 years ago 5
glad you like them all : )
i figured that if they suck, i would just delete them. most people seem to like them though : )
and honestly, i forget half of this stuff, so i make them for 'future me' - the one that has forgotten and re-watches old me (newer me?), so i have to be nice and soothing to my future self : )
patrickJMT 2 years ago 9
that's a good strategy, works out for all of us
Nanumir 2 years ago
"most people seem to like them though" No No Patrick. Everybody LOVES them. You are a great man. Thousands of students around the world are more grateful than you know. Thank you for the time and effort you put into these videos. They have saved the lives of many students.
yasthilmaharaj 2 years ago 82
For the last example on this video it is easier to use L'Hopitals on that limit by taking the ln of the limit instead of having to memorize that that limit equals e. You can show why it equals e.
goblue2733 2 years ago 3
your videos are brilliant patrick, just brilliant :)
by the way, i wanted to ask if n-th term theorem could be used on your 3rd example here.
emirdumani 2 years ago
Patrick. If I ever see you, I will kiss u on the mouth. This stuff is absolute greek and then you come in and put it all in layman's terms and voila, it's like magic. My brain has been having the "AHA" moment all day. Thank you sooooo very much dude. You make me wanna bake you cookies. That's saying something.
lorebetty 2 years ago
ahahahhaahah - that is awesome!
kisses + cookies = a good day
patrickJMT 2 years ago
@lorebetty "i will kiss u on the mouth" bwahaha.. but seriously i probably would too
janitarjanitar 1 year ago
So basically, series with (a sub n)^n, you can treat "a sub n" as your common ratio (r), and your (a) as 1 so, if r < 1, then it's convergent. Just right out of your first couple of videos.
RIght?
sircraigery 2 years ago
OMG I agree with Inferfire........it is plain scary that I understand all your root test/ratio test stuff, I have my final tomorrow and before these videos I thought I was screwed because i have absolutely NO idea what my prof is babbling about....I wanna seriously thank you so much!!!
dolce0me 2 years ago
Comment removed
leeiicc 2 years ago
is it scary that i understand this video??
Inferfire 2 years ago
probably not
patrickJMT 2 years ago
This has been flagged as spam show
1. Take a deep breath
2. Think about the one you love
3. Press ''F10'' 5 time
4. Send it to 5 video on youtube
5. Look at your background
brocklesnar20 2 years ago
in Europe this method is more oftenly reffered as Cauchy root test :)
vecr0 2 years ago
this is the stuff u need for college. so technically you flame yourself with tht
Stitchmaniac2 2 years ago 3
The sad part is we learned this in school!
sailormoonfanbase 2 years ago
what do you call when you multiply num and denom by 1/n, and one more thing patrick... why the denom ...(1+1/n)^n equals e?... it shouldnt be 1? thank you in advance
8osman8 2 years ago
(1+1/n)^n Is a notable limit witch equals e, look for it... and the 1/n multiply by num and denom is just a simplification, it doesn't affect the equation as you are using it in the top and the bottom..
leonlares 2 years ago
this is cool xD
thanks
tuestresfat 2 years ago
i just randomly clicked this video, and thank you for making my brain blow up.
pixelslayer00 2 years ago 6
me too xD
qwerrewq2 2 years ago
great lesson. Just one thing....series, in general, have many techniques and laws..
1) how do I know which technique to use when i see a formula?
2) what determines if a limit or series is convergent and divergent? when 0 is it always convergent? Please answer. Thank you
sportsfanful 2 years ago 3
Those are fantastic questions. I would love to see a video just to have those answered. Is there a possibility of having this done?
ohmannhey 2 years ago
How do i know tht i hv 2 use the root test 4 these kinda question
RadoAller 2 years ago
Normally you can use both ratio and root for these questions. it best to use root test for questions like (n)^n
MMX0710 2 years ago
WTH!?!?!?
Gararrad08 2 years ago
you lost me at "in this video".
pr0j3ctd00m 2 years ago 3
heck! you lost me when i saw the second paper!
Gararrad08 2 years ago 3
Hahahahahaha! I thought it was some drawing lesson! :P
tecoomexicano 2 years ago
u lost me too
JerkToTheMaxx 2 years ago
i love you
borispot 2 years ago 6
In the last example, the limit of n to inifity of 1^n is not just 1, but infinity. Over e, the series diverges by the root test.
Awsome job, I love watching your videos!
lau9876 2 years ago
1^(any power) is 1, so I think he was correct
21chuck 2 years ago 3
@21chuck 1^infinity =/= 1
ddog17billybob 1 year ago
i was just wondering if it was possible to use L'hospitals rule to work out hte limits here ? would it b appropriate?
mcykc 2 years ago
i'm pretty shocked at the last one how it turns into e. hmm... if i remember correctly, that's the compounding interst formula isn't it?
ahh i hate e, its so mysterious.. one day i'll have to sit and ponder :)
Ren520 2 years ago
well, 'e' is used in the continuous compounding formula.
and dont go hatin' on poor ole ' e ', it just wants to be useful like all the other numbers!
patrickJMT 2 years ago
I've never loved a man this much. No homo.
MPV839 2 years ago 3
dude ur a lifesaver. Thank you for all this. You make so much easier
hash2pat 2 years ago 2
OMG! thank you soooo much for posting this...watching this is way better than reading off a paper : )
sweetaquafire 2 years ago
is this also called as the Root rule comparison test?
chemworm3 2 years ago
You are awesome!
s2e3a4 3 years ago
i think you need to flip your fraction (n+1)/n
patrickJMT 3 years ago
i have a question on the second problem when u got to lim of (n/n+1)^n..isnt that e..y did u do all that other stuff like mult top and bottem by 1/x to get the 1/e?
tmj61 3 years ago
Great videos, they are really helping my preps for the exams! By the way, at 5.45 you say that 0*27=27, not that it matters, the answer will still be the same.
sindresaetre 3 years ago
ops, thanks!
i did that in another video too : )
i am making sure everyone is paying attention!
patrickJMT 3 years ago
Comment removed
vedranb 2 years ago
Actually, isn't 3^0 = 1?
So this would be 1 * 27 = 27?
Which is correct.
vedranb 2 years ago
If you look back to his solution you will see that (3^0)*(3^3)=27 and that is the same as yours.
roadZdiver 2 years ago
It was not a mistake...it is 3^(1/n) as n->infinity so it would be 3^0 which is 1.
It doesnt matter anyway...it was just to make it clear.
Thanks listening to me :)
n3vrax 3 years ago
Why did you multiply the top and bottom by (1/n)?
I know it lead to the (1/e) but... what made you do that?
tha1hustla1kidd 3 years ago
well, it is basically knowing that the n/(n+1) is the flip of (n+1)/n; that raised to a power of n has something to do with 'e'! i am seen that limit so many times now, that i just recognize it. so to answer your question, what made me think to do that is: experience!
sometimes one has to be shown what to do a few times before it sticks!
patrickJMT 3 years ago
at 8:35 you said that the limit of 1^n as n approaches infinity is 1!!
i thought 1^infinity was indeterminate!
aja431 3 years ago
1 to any real number power is 1.
the problem is if you have a function of the form [f(x)]^[g(x)] and f(x) is APPROACHING 1 (but not necessarily equal to 1).
limit notation is not very good; the standard notation is to use equality, when in reality it is just 'getting close' to that number (in most cases). eventually, one figures this out and just learns to deal with it : )
patrickJMT 3 years ago
Thank you Sir.
Alamagan2007 3 years ago
thanks so much
Lavar4u2nv 3 years ago
no problem
patrickJMT 3 years ago
you're the best it gets!
dleccord 3 years ago