L'Hopital's Rule ultimate study guide

Ultimate calculus tutorial on how to use L'Hopital's Rule (also spelled as L'Hospital's Rule) to evaluate limits with indeterminate forms? In this calculus tutorial, we will do 14 examples of using L'Hoptial's Rule to evaluate limits with indeterminate forms. Remember we can only use L'Hospital's Rule only if we have 0/0 or infinity/infinity. So if we encounter other indeterminate forms (i.e. 1^inf, 0^0, infinity - infinity, 0*infinity, inf^0), then we must somehow change the limit indeterminate forms first before using L'Hospital.

Big thanks to M.I's World for the following timestamps:
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

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[m.isworld]

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]

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

[angelvargas]

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

[nonentity]

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

[papkenhartunian]

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

[sarmadmaqsood]

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

[ChrisP]

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

[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.

[tinashechitate-by]

Thank you for this fine piece if art in maths

[eduardvalentin]

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

[gigathus]

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!

[turkix]

How theres only 57K viewers

You are a world class teachee

[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

[hydropage]

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

[chananleibler]

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?

[nightmarefredbear]

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

[srihari]

Slowly you became Confucius by teaching math😂

[danglersolutions]

please can you help me with this maths

[jayprados]

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

[ires]

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?