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
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
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?
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.
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!
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
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
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 🤣
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.
