A must watch Calculus series for all who are studying this subject. Clear presentation that includes organized content in a textbook format with intelligent, concise and step by step explanation of concepts and worked out examples. I enjoy learning from these videos. Thanks.
I love you, Professor Dave. I was teaching face-to-face classes with pencil-and-paper homework, just like back in the day, when suddenly, due to Covid-19, my classes are all online. I can make reasonably good math instructional videos, but not fast enough to keep up with four different courses in real time. I've been wandering UA-cam looking for good math videos to fit my learning objectives. This one is great. Thank you. --Professor Lisa.
Thanks for the online lecture man! My teacher at school is so hopeless, she couldn't taught L'Hospital because there's no L'Hospital explanation on textbooks
i love when some other smarty has done the maths to explain something that makes sense logically. I remember working towards this in a calc class back as a group in the day, before we worked on this.
At 5:42 , there is an error. If you express -x² to its reciprocal, you should get -1/x². So the solution should look like: (1/x) × (-1/x²) = -1/x³ If you differentiate this three times, you should arrive at an answer of 0/6, which is coincidentally also 0
Sorry Prof Dave but I evaluate your limit at 7:45 and my calculator says "Domain error" because Ln(0) gives domain error. How do you solve this? Thanks in advance.
Good. But is it logical to use L'Hopital's rule to find lim sin (x)/x, as we must know the limit before we differentiate sin(x)? There're so many similar examples.
You can't use L'Hopital's rule prove that lim (sin(x)/x) as x-->0 = 1. That's a circular argument because in order to prove that the derivative of sin(x) is cos(x) you need to know what value is lim (sin(x)/x) as x-->0.
What? Check out my tutorial on derivatives of trigonometric functions. You just plot the rate of change of sine and you get cosine. It couldn't be simpler.
@@ProfessorDaveExplains I was trying to say that we can't do a formal demonstration of the derivative of sin(x) using l'Hopital's rule. I didn't mean you did it on this presentation. btw, nice video and training exercices
Question regarding the limit of x(ln x) = 0, the graph of that function shows there is no limit from the left side, which is why you approached the limit from the right side, but I thought the rule of limits state that a limit can only exist if the limit exists from both sides? There is the limit of peace-wise functions but that still requires the limit of both functions to exist from both sides. I am just assuming there is some limit rule I am missing. Would you be so kind as to elaborate on this?
So we can't use the rule for the infinity over (infinity - infinity) ? Or we have to make this form infinity over infinity and the solve by L'Hospital?
0/infinity and infinity/0 will yield the limit to be 0 and infinity. An example of these function would be y=ln(x)/x and y=x/ln(x) as x goes to 0 from the right respectively. The limit would go to -infinity and 0.
I don't understand the last exercise (ln x/x^2): When deriving once, I get (1/x)/2x. However, the 1/x then gets derived to - 1/x^2, and I don't see where the minus sign went in the answer? Altough I get that your answer must be right since the function is curving up and not down and so it makes sense that the second derivative is positive when x -> infinity. Can anyone explain?
What I don't get is this: in the first example of sin x/x, the limit here is the definition of the derivative of sin x at x=0. Then in the same line he writes down cos x as the derivative of sin x which he's not supposed to know as that is exactly the thing he is calculating. Isn't he making justified assumptions?
There is no real life use, it's pure mathematics, but limits are the answer we get when we substitute the closest value to the variable, when we won't get a definete value when we substitute the exact variable.
For the question 1 at the end, why does limx->∞ 2x-9/6x+7 = limx->∞ 2/6 ? what happened to the -9 and +7 as I got to the part where i differentiate n wasnt sure what to do next. thank you for the great vid anyways
Hi. Have seen recently an MIT video which shows a failure in L ´Hospital rule. Lim for x tending to infinite from (x + cos x) / x Thanks I admire your videos
Did you mean (x + sin x) / x? (x + cos x) / x does not apply, because it does not produce an indeterminate form. L'Hopital's rule didn't fail. The failure was attempting to use it when it doesn't apply.
A must watch Calculus series for all who are studying this subject. Clear presentation that includes organized content in a textbook format with intelligent, concise and step by step explanation of concepts and worked out examples. I enjoy learning from these videos. Thanks.
I love you, Professor Dave. I was teaching face-to-face classes with pencil-and-paper homework, just like back in the day, when suddenly, due to Covid-19, my classes are all online. I can make reasonably good math instructional videos, but not fast enough to keep up with four different courses in real time. I've been wandering UA-cam looking for good math videos to fit my learning objectives. This one is great. Thank you. --Professor Lisa.
Your channel is absolutely amazing! Thank you for helping students everywhere!
Great video. You taught the rule in a way that saved me from going to the Hospital, lol.
Learning calculus for free is so enjoyable. Thanks Prof Dave!
Thanks a lot for your wonderful explanation..Now I am confident with this concept. 🇮🇳
Thanks for the online lecture man!
My teacher at school is so hopeless, she couldn't taught L'Hospital because there's no L'Hospital explanation on textbooks
lol, that would have sucked bad. I did had good lecture and note but the teacher pulled Eminem on us so hard to understand the lyrics
@@Lostwolf16 :')
Finally understood lopital rule after HOURS. Thank you professor!
I m from India 🇮🇳🇮🇳watching your lecture your videos very simply explain me the topic thank you so much sir for your efforts 🙏🙏🙏🙏🙏
This rule is just so neat!
Thanks Dave!
thank you professor Dave i got these lecture after 4 years at the day you uploaded and helped me to understand l'hopital's rule
thank you again
Thank you sir for your dedication and for making this free! 🙏
Your all videos are so informative n easy to understand.n tomorrow is my exam 😅.
Writing this bcz these videos helped me a lot.love from india❤️.
Thank you Professor Dave, please may you talk about the origin and the statement of L'Hospital rule.
i love when some other smarty has done the maths to explain something that makes sense logically. I remember working towards this in a calc class back as a group in the day, before we worked on this.
Thx for everything ♥️
no words can describe how grateful I am prof ❤
Thanks a lot for organizable, understandable and excellent explanation!!
No one can teach as like u sir😁😀😂😀👍👌
Thanks love from India!!
At 5:42 , there is an error. If you express -x² to its reciprocal, you should get -1/x².
So the solution should look like:
(1/x) × (-1/x²) = -1/x³
If you differentiate this three times, you should arrive at an answer of 0/6, which is coincidentally also 0
The best professor in the woooooorld we love youuuuu sir 🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹
Thanks so mach
Thi is an important
Concept in
Learning
Limit❤
@0:25 By sandwich theorem isn't it =1
You save me from Hospital
Your explanation is very nice professor ☺️
From your lecture I got to know many things. ❤
This man is a hero!
this was so helpful!
I love you professor, you always get me out of trouble, hope I meet you one day to thank you f2f
I finally get why asymptote of the range of function is that!!!!
I am so happppppppppppyyyyy!!!!!!!!!
Thank you sir...!! Its easy to understand properly
many many thanks
i've definitely subscribed , it helps me more than it helps you for sure!!!
Thank You! It was great!
Perfect teaching totally understood
Could you go over indeterminate products please?
Sorry Prof Dave but I evaluate your limit at 7:45 and my calculator says "Domain error" because Ln(0) gives domain error. How do you solve this? Thanks in advance.
Same question
Oh got it now
Because it's 0+
Thank youuu 🤗🤗
stupid girl
@@tse278 bruh moment 69420
You're the great sir dave
Many many thanks, sir !!
I am gonna recommend this playlist to all the suffering 11th grade friends i have xD
this is absolutely awesome thanks man
thankyou so much bro!
Thank you!💜
Good. But is it logical to use L'Hopital's rule to find lim sin (x)/x, as we must know the limit before we differentiate sin(x)? There're so many similar examples.
thanks
You can't use L'Hopital's rule prove that lim (sin(x)/x) as x-->0 = 1. That's a circular argument because in order to prove that the derivative of sin(x) is cos(x) you need to know what value is lim (sin(x)/x) as x-->0.
What? Check out my tutorial on derivatives of trigonometric functions. You just plot the rate of change of sine and you get cosine. It couldn't be simpler.
@@ProfessorDaveExplains I was trying to say that we can't do a formal demonstration of the derivative of sin(x) using l'Hopital's rule. I didn't mean you did it on this presentation. btw, nice video and training exercices
I am 10 years old and finish the whole calculus course smart ha
पागल हो क्या
Wow! I finally get it!!!
Thanks sir your my hero
Which hospital is that?
It’s the one in France
The one you go to when you think about this too much and get an aneurysm
Question regarding the limit of x(ln x) = 0, the graph of that function shows there is no limit from the left side, which is why you approached the limit from the right side, but I thought the rule of limits state that a limit can only exist if the limit exists from both sides? There is the limit of peace-wise functions but that still requires the limit of both functions to exist from both sides. I am just assuming there is some limit rule I am missing. Would you be so kind as to elaborate on this?
Professor thank u, From 🇮🇳 India😢
Excellent
YOU SAVED ME
So we can't use the rule for the infinity over (infinity - infinity) ?
Or we have to make this form infinity over infinity and the solve by L'Hospital?
Super sir
thanks again sir
Thank you sir
Sir if it is 0/infinity or infinity/zero,,would we apply the L.rule?
Topi Ado no sir
@@cristiansantos5070 girl#me
Topi Ado sorry!
0/infinity and infinity/0 will yield the limit to be 0 and infinity. An example of these function would be y=ln(x)/x and y=x/ln(x) as x goes to 0 from the right respectively. The limit would go to -infinity and 0.
I don't understand the last exercise (ln x/x^2): When deriving once, I get (1/x)/2x. However, the 1/x then gets derived to - 1/x^2, and I don't see where the minus sign went in the answer? Altough I get that your answer must be right since the function is curving up and not down and so it makes sense that the second derivative is positive when x -> infinity. Can anyone explain?
love you dave
What I don't get is this: in the first example of sin x/x, the limit here is the definition of the derivative of sin x at x=0. Then in the same line he writes down cos x as the derivative of sin x which he's not supposed to know as that is exactly the thing he is calculating. Isn't he making justified assumptions?
look earlier in the calculus playlist for a tutorial on finding the derivatives of trigonometric functions, it's quite well derived
Thank u sir!
Thank you jesus
Amazing
Hey Dave, I'm a bit confused
Why didn't you use the quotient rule to solve for limx->0 (e^x/x^3)
Thank you, hope to hear from you soon
Rule applies only for when you take derivatives of quotients not for limits. 💜
How to define a limit using real life examples
there are no real life examples! this is mathematics.
There is no real life use, it's pure mathematics, but limits are the answer we get when we substitute the closest value to the variable, when we won't get a definete value when we substitute the exact variable.
It's important but really often more background for integrals and derivatives which 100% have real-world applications :)
this channel def the best at explaining shit
what about when x approache to zero for absolute value of x over x does the rule work?!
Lim (x->inf, (x+cos(x))/x ) is indeterminate, but L'hopital's rule fails.
Bro casually solves infinity 🎉
love you sir
For the question 1 at the end, why does limx->∞ 2x-9/6x+7 = limx->∞ 2/6 ? what happened to the -9 and +7 as I got to the part where i differentiate n wasnt sure what to do next. thank you for the great vid anyways
He took the derivative again
derivative of 2x-9/6x+7 = 2/6
Hi. Have seen recently an MIT video which shows a failure in L ´Hospital rule. Lim for x tending to infinite from (x + cos x) / x Thanks
I admire your videos
Did you mean (x + sin x) / x?
(x + cos x) / x does not apply, because it does not produce an indeterminate form.
L'Hopital's rule didn't fail. The failure was attempting to use it when it doesn't apply.
just came to know how to pronounce this word !!
i loved it
Thank you Jesus
Bro wtf💀
4:28 I guess here L'hopital rule will also give correct answer .
what if g(x)=1 for example and we apply this, we get f'(x)/0 if defined then it's infinity. just guessing not sure, HELP
Thank 🥰
I still don't get it
I got it after 6th time 🥹
It ain't that hard by solving problems you will understand is better. 😊
You're awesome
very bad
I thought this was going to show why L'Hopital's rule works (graphically? I don't know).
Done.
I dont know why sinx derivative to cosx
Check out my tutorial on derivatives of trig functions, I derive them graphically.
l'hospital rule
i love infinity
i think the second comprehansion questoin is wrong because its ans is not maching mine i have done several times
I wrote it.
Great
4:30 lim f(x)*g(x) How To Convert To Usable L'Hopsital Rule
How computer and human solve the no solution problem?
2:15 Actually you can’t use L’Hop here
how so?
You need to give the reason to prove you are right, rather than said' you are wrong'
I must notice that he's not L'Hospital
Yeah, I'm Dave. I thought I made that clear in my intro!
I am in class 11 i am from india
It is not in our syllabus but we use this as a short cut in our syllabus 😎
good sir.
i
L'Hospital? Isn't it spelled L'Hopital?
Both are correct actually.