I come from your calculus 3 videos and just wanted to say you are an amazing professor. I don’t know where I would be with out you. Thank you so much for doing a fantastic job at teaching. Your videos you produced back in 2016 are still relevant in 2020 and make a difference in many lives. You are better than any other math professor I have ever had in my life. You make the subject easy to understand and enjoyable. Again thank you so much for what you are doing you have changed my life and many others. Keep up the amazing work hope to use your videos for the rest of the classes I have to take.
I remember this a silly way. If you take the factory out of town, there will be a hole left behind But If you can’t take the factory out, the way the town shrinks or grows is determined by the mean owner, the ASSymptote .
Haven't been to school in 5 years. Due to inflation.....I have decided to go back to school. On a whim, I started a class on the 31st(Calc II) two days after I decided to do so. I am now on video 43 of 115 of this precalc playlist. It has helped a lot to refresh. First assignment due soon. Time to buckle up.
Professor Leonard, thank you for another power selection and explanation on finding asymptotes and holes of rational function. These videos prepare students for graphing all types of functions in Calculus.
You have NOOOO idea, he literally saved my life I probably would've gotten sick due to stress or something. Thanks to him I was able to relax and truly learn! I'm on my way to becoming a scientist/professor thanks to him!
Professor Leonard Your videos are the only reason I haven't failed out, thank you so much for all that you do. Is there any chance of you continuing the Differential Equations Series?
Professor Leonard, why can't (2x + 3) / (3x + 1) be written as (x + 3/2) / (x + 1/3) ??? Aren't they equivalent factors? And yet they give different points when you plug 4 into x.
@@milandukic4080 Even though both will give you the same x-coordinate. They are not the same **graph**. To make them the same graph, you have to remember to multiply by the 2 that’s been factored out.
Hi, do you have any videos on graphing these kinds of functions but with roots? I'm not having any luck finding goood material on that anywhere and if you explained that, I'd be able to understand it! Thanks! Keep up the great videos! :)
Professor, I know you are no where near this subject but I was looking at your previous videos on error approximation and cant find an example to tackle the problem I am doing. I am given P3(X)= X - X^3/6. The question asks me to use this to approximate the error if P3(X) is used to approximate sin(x) at x=.1 I was thinking of of ways to tackle this but I am just lost. Please help me :( pls and tyyyy
@@user-bl9ir7xo4n You should use maybe a book. So if you are studying precalculus like i am, you would use your textbook problems as practice. make sure that you have a book and its answers
Professor, I want to join your you tube channel since I know that I am a kid studying in class 9 but I can teach students. I know higher Mathematics in a really really good manner so pls let me join your channel and teach . Pls if you don't believe ask professor of REAL INSTITUTE OF MATHS , HE IS IN AN INDIAN AND I AM ALSO AN INDIAN.
I come from your calculus 3 videos and just wanted to say you are an amazing professor. I don’t know where I would be with out you. Thank you so much for doing a fantastic job at teaching. Your videos you produced back in 2016 are still relevant in 2020 and make a difference in many lives. You are better than any other math professor I have ever had in my life. You make the subject easy to understand and enjoyable. Again thank you so much for what you are doing you have changed my life and many others. Keep up the amazing work hope to use your videos for the rest of the classes I have to take.
the only teacher that makes me excited to learn math.
I feel It too
I agree
I watch all the ads! So I can play my part to appreciate you
I remember this a silly way.
If you take the factory out of town, there will be a hole left behind
But
If you can’t take the factory out, the way the town shrinks or grows is determined by the mean owner, the ASSymptote .
Haven't been to school in 5 years. Due to inflation.....I have decided to go back to school. On a whim, I started a class on the 31st(Calc II) two days after I decided to do so. I am now on video 43 of 115 of this precalc playlist.
It has helped a lot to refresh. First assignment due soon. Time to buckle up.
Love this man, calc videos saved my life so I always like any new video now.
Hunter Branch he is a life savior and an amazing professor currently taking calc 3 and I watch his videos over my own professors
Adam Potter same here 😂
Loveliest teacher on the Earth..❤
Always thankful for Calculus..!!
Thanks! You’ve kept the same patient tone during all these videos 💯.
Professor Leonard, thank you for another power selection and explanation on finding asymptotes and holes of rational function. These videos prepare students for graphing all types of functions in Calculus.
A truly wonderful hunk of math professor you are
I haven’t gotten into uni yet but I already feel this man is going to be a lifesaver
You have NOOOO idea, he literally saved my life I probably would've gotten sick due to stress or something. Thanks to him I was able to relax and truly learn! I'm on my way to becoming a scientist/professor thanks to him!
He definitely is
I wish I have money to donate... His help is priceless. wait till you get to calc 2+3
36:37 If you long dive all the way through, you can tell whether the function is above or below the asymptote at the infinities.
You are really REALLLLLLLLLY BEAUTIFUL Teacher keep it up
He is excellent. I wish I had him as my college professor 40 years ago
Thank you so much! this helped get a A on my exam!
Keep kicking butt Professor Leonard!!!
Wow! Almost one or two videos per day. I'm impressed.
Thanks for the lessons Prof Leonard
Everything here makes sense! Can't thank you enough.
Professor Leonard Your videos are the only reason I haven't failed out, thank you so much for all that you do. Is there any chance of you continuing the Differential Equations Series?
42:53 I want this printed on a tee.
Now you can all tell your friends that "You don't know your asymptote from a hole in the graph."
Professor Leonard, why can't (2x + 3) / (3x + 1) be written as (x + 3/2) / (x + 1/3) ??? Aren't they equivalent factors? And yet they give different points when you plug 4 into x.
Did you find answer to this? I can't understand it either
@@milandukic4080 Yes, I did. They are only equivalent if you remember that (x + 3/2) / (x + 1/3) has a 2 that’s been factored out.
@@milandukic4080 For example, (x + 3/2) is not equivalent to (2x + 3). But 2(x + 3/2) is equivalent to (2x + 3).
@@milandukic4080 Even though both will give you the same x-coordinate. They are not the same **graph**. To make them the same graph, you have to remember to multiply by the 2 that’s been factored out.
What if the leading coefficient for the numerator is bigger than the denominators with a higher power
Ex)
(2x+2)/
(X^2+1)
Damn good professor
Big Lenny is the Tom Platz of Math
Hi Professor Leonard, are you going to do a linear algebra course within the next year or so? Thanks!
Hi, do you have any videos on graphing these kinds of functions but with roots? I'm not having any luck finding goood material on that anywhere and if you explained that, I'd be able to understand it! Thanks! Keep up the great videos! :)
Professor, I know you are no where near this subject but I was looking at your previous videos on error approximation and cant find an example to tackle the problem I am doing. I am given P3(X)= X - X^3/6. The question asks me to use this to approximate the error if P3(X) is used to approximate sin(x) at x=.1
I was thinking of of ways to tackle this but I am just lost. Please help me :( pls and tyyyy
The hole point of a missing point 🥴👌🏻
How can l practice everything l have learned. I self learn so l don't follow a teacher and don't receive homeworks.
did you solve this? I'm having the same problem
@@user-bl9ir7xo4n You should use maybe a book. So if you are studying precalculus like i am, you would use your textbook problems as practice. make sure that you have a book and its answers
I love you so much
Has anyone ever told you you look like a really buff Stephen Colbert?
Sir I am the biggest fan of your teaching method.
I request you to start Linear algebra...please...
Offering knowledge for free....that's where it's at....yup Professor Leonard is getting laid.
Professor, I want to join your you tube channel since I know that I am a kid studying in class 9 but I can teach students. I know higher Mathematics in a really really good manner so pls let me join your channel and teach . Pls if you don't believe ask professor of REAL INSTITUTE OF MATHS , HE IS IN AN INDIAN AND I AM ALSO AN INDIAN.