Calculus teacher vs L'Hopital's rule students

If you are also a calculus teacher, then you know most students will just use L'Hospital's rule for every limit after they learn the rule. So let's investigate the limit as x goes to infinity of (the integral from 0 to x of sin(t)*e^cos(t))/x and see why we cannot use L'Hôpital's rule. This is a great challenging limit problem for your calculus students! #calculus #blackpenredpen #challenge

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Thank you all!

[joysanghavi]

The original problem was equivalent to finding the average value of the function

[jim]

Real ones never forget definition of a derivative 🗣

[isaacclark]

Let's be honest. No student really wants to use the definition of derivative even before they learn the power rule. They do it because we insist that they use it.

[DARKi]

The funny part is that the final step, with 2 and n canceled, is also doable with l'Hopital, in the end

[Nxck]

I got 2/pi * sinh(1) using Fourier series

[Morgyborgyblob]

First time I encountered L'Hopital's Rule was in a test where the question said, "without using L'Hopital's Rule". I was like, "uh, cool...wasn't going to use that thing I've never heard of anyway, but now I wanna know what it is"

[Ninja]

I remember michael penn doing a video about this topic and the example he gave is x/(x+sinx) as x->inf. This limit is 1 but using L’H rule will give you DNE.

The full L’H rule is that the limit of f’(x)/g’(x) must exist first before we can conclude that the limit of f(x)/g(x) will be the same.

[Aakarshan]

Solving a maths problem : 😔
Solving a maths problem with e or π : 😩
Solving a calculus problem with e or π : 😭😭

[MidnightToker]

Great explanation 🙏🏻

I have to say that from the first video of yours that I watched it was clear that you are a great teacher, and I was impressed and satisfied with your presentation. I actually stumbled on one of your other channels, which led to another, at which point I decided to search bprp to see if there were more channels. That led me to this channel which appears to be your main, though I intend to search for more just in case, and want to check out the content you've been through on the channels I've found already.

I've always had a love for math. Even as a child, before going to school, I would look at my older cousin's homework and try to solve her math equations, and even taught myself how to read and write. I would take every opportunity I could to absorb knowledge in a wide range of subjects, observe and analyze everything I saw, and to think about how things work and how they connect. I even managed to learn basic trigonometry in 3rd grade by accident while doodling in class, during "free time" of course. I never had access to higher education in school and unfortunately didn't do much on my own after school to learn more, but I've always been interested in learning more.

There were many things I wasn't taught, simple and complex, due to transferring to several schools, often in the middle of a term. A video on your channel was actually the first time I've ever been shown long division and, as I mentioned previously, I never took the time or initiative to learn it on my own. I was already aware of the rest of the things you discussed in the video but just from your explanation of long division it made perfect sense to me and motivated me to look through more of your content because I'm eager to learn more about complex math, terminology, and formulas that I never learned.

I tried to get my school to offer a calculus or trigonometry class but they declined saying there wouldn't be enough students participating. 4th or 5th grade was, unfortunately, the last time I actually learned anything at school, in the subject of math. While it made getting a good grade and high test scores easy, I lost my joy for math at some point.

Unfortunately I never went to college, and can't afford to now, but that's never stopped me from seeking knowledge and learning from others. Again, I'm glad I found your channels and I'm grateful for your time and effort you spent into making these videos. You make things easy to understand and I even enjoyed seeing your lessons regarding the things I already knew. Many people are uninterested, impatient, or bored with math, maybe because they didn't have the right teacher or maybe they simply don't care or realize its value but, for the people who are interested in math for fun or for real situations, this content is invaluable.

Thank you for what you're doing and I apologize, to whoever has made it this far, for the long comment. Keep up the great work, I look forward to seeing more of what you do 🙏🏻

[zapking]

Alternate title, calculus teacher versus physics student

[paranoyd]

Nice video. You can just do the average height of the square of area e-1/e. Since it has a length of pi, divide area by length to get height. The pi sectors are all the same, to get the area from 0 to x just do (e-1/e)/pi*x. Dividing by x in the limit, you get (e-1/e)/pi. Boom. Done.

[hadhad]

I use L'Hopital's rule when my bank account is 0 and my paycheck is 0 and I have to do 0/0 😅
But yeH I love it always trying to use it's I was tutoring somebody math and they had to do a limit and I said let's use L'Hopital's rule
They didn't know it yet never heared of it 😂

[sergeygaevoy]

There another example: lim((x - sin(x))/x) when x->inf = 1
It is [inf/inf] but L'H gives us lim((1 - cos(x))/1) x->inf. It doesn't exist BUT its AVERAGE value is 1 too!

[rodrigomack]

Calculus teachers when they give students tools to make their lives easier, and they use those tools to make their lives easier

[maxrs]

to use LH rule u have to prove that the functions are smooth and continuous, top one obviously isnt

[sazzadulkader]

Sir, I'm watching from Bangladesh 🇧🇩.

[Ashutosh-gnux]

Hello do yo have any playlist of learning calculus of your videos,
it would be very helpful if you share, and my stage is just a beginner need to know every possible thing .

[leonardobarrera]

I am going to see, because it can be only members!!!
Xd

[romanbykov]

it's just another Euler's identity (connecting e, pi and -1)! Awesome, dude!

[arefinshuvo]

sir are you from japan or china?Or from other countries?