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 TH-cam looking for good math videos to fit my learning objectives. This one is great. Thank you. --Professor Lisa.
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.
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
Hi Dave! I believe we cannot use L’Hôpitals rule for sin(theta)/theta, this is because we need to know the derivative of this in order to use l’hopital’s, thus we cannot use l’hopitals for us to find the derivative… Am I right? How can we calculate this derivatives without using L’Hôpital’s rule then? Great video!
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
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.
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?
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?
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?
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
@JinkunYan The thing is, to rigorously prove that d/dx (sin (x)) = cos(x), you should actually use the limit definition, not just plot some points. While you're proving with the limit, you'll have to know the result of lim_(h->0) sin(h)/h Similarly, you'll also need to know lim_(h->0) (cos(h) - 1)/h The traditional way to prove these limits is to geometrically show that, for an angle θ near 0 1 >= sin(θ)/θ >= cos(θ) As θ approaches 0, the expression is "squeezed" by 1 on both sides, so it has to be 1 From here, the other limit is not that bad, you can use the pythagorean identity and use the result of this limit we've found So basically, when you use L'Hôpital's rule, you've to know already the derivative of sine, but to show what the derivative for sine is, you actually have to know the result for this limit already
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.
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.
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 TH-cam looking for good math videos to fit my learning objectives. This one is great. Thank you. --Professor Lisa.
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.
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.
Thanks a lot for your wonderful explanation..Now I am confident with this concept. 🇮🇳
Learning calculus for free is so enjoyable. Thanks Prof Dave!
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 :')
Thanks Dave!
This rule is just so neat!
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
Thanks a lot for organizable, understandable and excellent explanation!!
Finally understood lopital rule after HOURS. Thank you professor!
Thank you sir for your dedication and for making this free! 🙏
Thanks love from India!!
Thx for everything ♥️
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.
Thank you so mcuh for the explaination! Was very easy to follow along and understand L'Hospital's rules
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❤️.
no words can describe how grateful I am prof ❤
Thank you Professor Dave, please may you talk about the origin and the statement of L'Hospital rule.
Thanks so mach
Thi is an important
Concept in
Learning
Limit❤
many many thanks
I m from India 🇮🇳🇮🇳watching your lecture your videos very simply explain me the topic thank you so much sir for your efforts 🙏🙏🙏🙏🙏
this was so helpful!
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 🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹🌹
Your explanation is very nice professor ☺️
Thank you sir...!! Its easy to understand properly
From your lecture I got to know many things. ❤
No one can teach as like u sir😁😀😂😀👍👌
This man is a hero!
Thank youuu 🤗🤗
stupid girl
@@tse278 bruh moment 69420
i've definitely subscribed , it helps me more than it helps you for sure!!!
Perfect teaching totally understood
I finally get why asymptote of the range of function is that!!!!
I am so happppppppppppyyyyy!!!!!!!!!
thanks
I love you professor, you always get me out of trouble, hope I meet you one day to thank you f2f
Thank You! It was great!
You're the great sir dave
this is absolutely awesome thanks man
thankyou so much bro!
Thanks sir your my hero
Thank you!💜
Thank you sir
@0:25 By sandwich theorem isn't it =1
Excellent
Hi Dave!
I believe we cannot use L’Hôpitals rule for sin(theta)/theta, this is because we need to know the derivative of this in order to use l’hopital’s, thus we cannot use l’hopitals for us to find the derivative… Am I right? How can we calculate this derivatives without using L’Hôpital’s rule then?
Great video!
You save me from Hospital
thanks again sir
Wow! I finally get it!!!
Could you go over indeterminate products please?
Super sir
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
Thank u sir!
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+
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.
Many many thanks, sir !!
I am gonna recommend this playlist to all the suffering 11th grade friends i have xD
Amazing
I have a question: How can we know which function we are inverting and placing under the other? Please answer me
love you dave
love you sir
Professor thank u, From 🇮🇳 India😢
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
YOU SAVED ME
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?
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
I am 10 years old and finish the whole calculus course smart ha
पागल हो क्या
Thank you jesus
Thank 🥰
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?
i loved it
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?
what about when x approache to zero for absolute value of x over x does the rule work?!
You're awesome
very bad
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. 💜
Done.
this channel def the best at explaining shit
Great
Thank you Jesus
Bro wtf💀
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
4:28 I guess here L'hopital rule will also give correct answer .
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. 😊
Lim (x->inf, (x+cos(x))/x ) is indeterminate, but L'hopital's rule fails.
i love infinity
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'
@JinkunYan The thing is, to rigorously prove that d/dx (sin (x)) = cos(x), you should actually use the limit definition, not just plot some points.
While you're proving with the limit, you'll have to know the result of
lim_(h->0) sin(h)/h
Similarly, you'll also need to know
lim_(h->0) (cos(h) - 1)/h
The traditional way to prove these limits is to geometrically show that, for an angle θ near 0
1 >= sin(θ)/θ >= cos(θ)
As θ approaches 0, the expression is "squeezed" by 1 on both sides, so it has to be 1
From here, the other limit is not that bad, you can use the pythagorean identity and use the result of this limit we've found
So basically, when you use L'Hôpital's rule, you've to know already the derivative of sine, but to show what the derivative for sine is, you actually have to know the result for this limit already
I wrote it.
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 :)
I dont know why sinx derivative to cosx
Check out my tutorial on derivatives of trig functions, I derive them graphically.
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
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 thought this was going to show why L'Hopital's rule works (graphically? I don't know).
How computer and human solve the no solution problem?
i think the second comprehansion questoin is wrong because its ans is not maching mine i have done several times
good sir.
Bro casually solves infinity 🎉
i
L'Hospital? Isn't it spelled L'Hopital?
Both are correct actually.
Why do I pay for university?