L'Hopital's Rule ultimate study guide

[@m.isworld2562]

0:00 start of the video 0:07 x-sinx/x-tanx as x goes to 0 3:16 (arctanx)^2/x as x goes to 0 4:32 ln(x^3-8)/ln(x^2-3x+2) as x goes to 2+ 9:45 x/(lnx)^3 as x goes to infinity 13:13 x^2+4x+3/5x^2-x-4 as x goes to infinity 15:48 ln(e^x+1)/(4x+1) as x goes to infinity 18:52 x^(1/(x-1)) as x goes to 1+ 24:05 x^(1/(1+lnx)) as x goes to 0+ 27:08 (x/(x-1)-1/lnx) as x goes to 1+ 31:55 (1/sinx - 1/x) as x goes to 0+ 34:36 ln(x^2-1)-ln(x^3-1) as x goes to infinity 36:42 sqrt(x^2+3x+1)-x as x goes to infinity 39:23 e^x times sin(1/x) as x goes to infinity 43:47 xarctan(x) as x goes to infinity im not sure if these are all correct timestamps

[@bprpcalculusbasics]

Thank you very much!

[@unoqueen_]

if I get an A on my test I owe it to u

[@angelvargas9042]

Its crazy watching this guy and the organic chemistry guy. Currently studying for my engineering license and need to watch these videos to remember basic cal properties. I remember watching you and the organic chemistry guy 7 years ago at the junior college. Its such a trip to still watch your videos many years later. I remember struggling so bad on this stuff and after just completing reinforced concrete design. I realize that it wasn't so bad. I guess what I'm trying to say is that as the years go on, your going to realize that this stuff wasn't so bad and you'll just honestly laugh at yourself lol. This is the reason why many people don't go to college because with each new semester, comes new emotions, new struggles and most importantly a new version of you. Each semester we all have ever taken continues to add more value to your life and increase your critical thinking skills. You may or may not use calculus for your career but the critical thinking skills will reveal itself when you need it the most. Don't give up on your educational journey. Your future self is waiting for you on the other side. - The engineer turned PreMed

[@agootson]

They're the only English ppeakers who break it down so well. The rest are Indians who lecture in Hindi.

[@bprpcalculusbasics]

Could someone please help with the time stamps? It’s late and I haven’t gotten much sleep lately. Thank you.

[@nonentity168]

We are blessed to have online educators like you. Thanks a lot

[@hobelarge6389]

My brother, your subtle and automatic handling of the markers, is magic. The most distracting part of this isnt rhe pokeball, its how the markers move like liquid in your hands. A master at work

[@papkenhartunian186]

One of the best lectures that I have ever attended. Bravo!

[@sarmadmaqsood727]

Thank you for this! Now I have more practice using L'Hopitals!

[@mikejackson19828]

Great video, Steve!

[@ChrisP999]

Absolute wonderful sight, so glad to many examples to see different approaches to these. Keep it up!

[@dpmike32819]

Excellent selection of problems

[@xboxlox]

14:31 It's also possible to simply multiply both the numerator and the denominator by (1/n^2). Everything will be eliminated as it approaches infinity, except for 1 in the numerator and 5 in the denominator, which will result in (1/5). But still, this is a very good video. Thank you very much! I am watching with great joy.

[@xboxlox]

hahahah noooo i am not going to delete this hahaha ok you have done that way thank you

[@nightmarefredbear7739]

0:06 Problem 1 3:15 Problem 2 4:33 Problem 3 9:45 Problem 4 13:13 Problem 5 15:47 Problem 6 18:52 Problem 7 23:58 Problem 8 27:08 Problem 9 31:56 Problem 10 34:35 Problem 11 36:42 Problem 12 39:25 Problem 13 43:47 Problem 14

[@eduardvalentin830]

18:52 sub u=1/x-1 and you get the definition of e. Nice!

[@tinashechitate-b6y]

Thank you for this fine piece if art in maths

[@muslimguy1068]

Thanks for the explanation man!

[@sri78hari]

Slowly you became Confucius by teaching math😂

[@boudescotch]

After the x/(lnx)³ I goes look the graph of the function and this is pretty surprising that the limit as x goes to infinity is infinity

[@memebaltan]

Me too, it actually slowly rises after dipping at around x=20.086

[@khaledalbijawy]

you are absolutely legend

[@jayprados1089]

This man is the son of the old guy from Harry Potter

[@turkix4809]

How theres only 57K viewers You are a world class teachee

[@acopiae]

and just 700 likes. must be too niche

[@gmoney_swag1274]

his main channel has millions of subscribers (blackpenredpen)

[@gigathus3314]

Wonderful video man, thank you so much for the help! I do have a question though, in regards to the problem at 27:08 - Why couldn't we simply do L'Hopital's Rule to both ends of the difference instead of simplifying and making an equal denominator? If we do L'Hopital's Rule to both ends of the difference, we get that the Limit is equal to "0" instead of 1/2. I'm wondering why this doesn't work because from what I remember, if you are taking the limit of an expression that includes addition and/or subtraction, you can split the expression into the sum of limits like this: (lim x->1^+ (x/(x-1))) - (lim x->1^+ (1/lnx)). Why can't L'Hopitals Rule be applied like this? Thank you so much for the video you are saving so many students grades!

[@npsiddhant3474]

If you apply the limit it becomes 1^(+)/1^(+) - 1 =a lets say and 1/ln(0^+)=b So a-b The a term becomes ∞ and the B term 1/(-∞) i.e 0 and then a-b becomes ∞-0

[@ruchigaur5127]

Perfect video

[@JoyJohn-ux3cm]

I have assignment, can u help me?

[@danglersolutions2]

1/x - 1/sinx as x approaches 0

[@chananleibler6901]

In number 7 isn’t 1+^inf always infinity, since if you think about it 1+ ≈1.0000…1 and if you multiply that by itself infinite times it will approach infinity? And similary wouldn’t 1-^inf approach 0?

[@gileadedetogni9054]

The ideia is that the 1+ can be closer of 1 in a way "more stronger" than the infinity

[@abdullahkamel2428]

i fucking love this guy

[@margot947]

Thank you, so much for sharing

[@isharauditha4257]

you are the saviour

[@danglersolutions2]

please can you help me with this maths

[@hydropage2855]

Professor Chow, the worksheet link was taken down. Just wanted to inform you

[@bprpcalculusbasics]

Thanks for letting me know. The file is okay but I think many people have been finding bit.ly links not working for them. So here's the original link (long link, lol) 936933f9-1455-44ce-b414-4d0b35a6c090.filesusr.com/ugd/287ba5_fc19d8f3e1a94c4295298047578e2197.pdf and I also changed it in the description. Thanks.

[@mohamedbelcaid2023]

Ingenious 🎉

[@omarhmidani6063]

2:00 just seen the function and found the solution

[@KgopotsoMoloto-vx2rq]

Thank u sir😁😍

[@jannawang9279]

why do you have a pokemon ball?

[@MuhammadBilal-pi3lo]

Because his brain power of Maths lies there

[@kittynpaws6580]

It's his mic in disguise lol

[@BSL1515]

Thanks sir

[@ires3731]

for q11, when u bring the limit inside, why is it approaching 0 from the right? shouldn’t it just be 0 since it’s the limit from just infinity?

[@acopiae]

presumably to keep the number positive, otherwise you have the log of a negative number.

[@gileadedetogni9054]

That's because you're approaching positive infinity, so you get "0+"

[@pogisomakaba4829]

Isn't number 7 supposed be e^-1

[@nelsonberm3910]

you are a mega g

[@boonga585]

5:41

[@jimmycatyen]

Question 12 We can solve it by looking 3-0/2=3/2

[@aditidump]

can u pls xplain further?

[@Shawon00s]

Thank you...

[@azuxs]

Number 13 is 0, not infinity.

[@bprpcalculusbasics]

It's infinity. www.wolframalpha.com/input?i=limit+of+e%5Ex*sin%281%2Fx%29+as+x+goes+to+inf

[@azuxs]

@@bprpcalculusbasics Could you explain further? How come after putting sin(1/x)/e^-x and you plug in infinity = sin(0)/infinity = 0/infinity = 0.

[@boonga585]

26:39

[@散华-l9m]

just have fun with math for around 45 minutes

[@pardeepgarg2640]

Lopital's Rule 👁️👄👁️ YaY

[@walidslimani]

there is a lot you can solve them without l'hopitals rule

[@petereziagor4604]

Integration rules please

[@Cycy98MinecraftFR-xh9lr]

I think it's also spell L'Hôpital's rule, I think it because hopital seem French.

[@woshibaba428]

I love you

[@hipolitonovido8651]

Too fast for me lol

[@HeadBandNash]

😂😂

[@solitary6002]

Why work so much for the question 10? x tends to 0+....sin x = x for a very very small angle... Thus 1/sin x = 1/x Thus lim x tends to 0+ 1/sin x - 1/x = 0 That's what I though on seeing the question 🤣

[@isaquepim4555]

The classic engineer approach 🤣 but try it for 1/sin(x)^2 - 1/x^2

[@ZipplyZane]

To be more explicit: this works, but only with linear terms. It doesn't work the second you raise sin(x) to any power. The reason it works is because of the Taylor expansion of sine. If you have an exponent of 1, all the other terms are insignificant. Michael Penn (the math teacher) has a video on this. It's called "When This Approximation Goes Wrong," and shows sin x ≈ x in the thumbnail.