Finding Asymptotes and Holes of Rational Functions (Precalculus - College Algebra 43)

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  • Опубликовано: 24 дек 2024

Комментарии • 49

  • @adamt6024
    @adamt6024 4 года назад +20

    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.

  • @madebyyuzz
    @madebyyuzz 8 месяцев назад +4

    the only teacher that makes me excited to learn math.

  • @nehaljhirmaria
    @nehaljhirmaria 4 года назад +12

    I watch all the ads! So I can play my part to appreciate you

  • @3dtour
    @3dtour 4 года назад +27

    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 .

  • @relyt22ful
    @relyt22ful 2 года назад +2

    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.

  • @hunterbranch8458
    @hunterbranch8458 4 года назад +23

    Love this man, calc videos saved my life so I always like any new video now.

    • @adamt6024
      @adamt6024 4 года назад +6

      Hunter Branch he is a life savior and an amazing professor currently taking calc 3 and I watch his videos over my own professors

    • @audi.6106
      @audi.6106 4 года назад +5

      Adam Potter same here 😂

  • @AdnanKhan-mm6bo
    @AdnanKhan-mm6bo 4 года назад +1

    Loveliest teacher on the Earth..❤
    Always thankful for Calculus..!!

  •  11 месяцев назад

    Thanks! You’ve kept the same patient tone during all these videos 💯.

  • @georgesadler7830
    @georgesadler7830 2 года назад

    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.

  • @ebog4841
    @ebog4841 4 года назад +4

    A truly wonderful hunk of math professor you are

  • @hotyeahsus8343
    @hotyeahsus8343 4 года назад +19

    I haven’t gotten into uni yet but I already feel this man is going to be a lifesaver

    • @theaveragemegaguy
      @theaveragemegaguy 4 года назад +7

      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!

    • @audi.6106
      @audi.6106 4 года назад +3

      He definitely is

    • @asemyamak3984
      @asemyamak3984 4 года назад

      I wish I have money to donate... His help is priceless. wait till you get to calc 2+3

  • @slr150
    @slr150 3 года назад

    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.

  • @stircrazygenius8464
    @stircrazygenius8464 4 года назад +6

    You are really REALLLLLLLLLY BEAUTIFUL Teacher keep it up

  • @jimjim2119
    @jimjim2119 2 года назад

    He is excellent. I wish I had him as my college professor 40 years ago

  • @bellringer7747
    @bellringer7747 4 года назад +2

    Thank you so much! this helped get a A on my exam!

  • @ProfChaoss
    @ProfChaoss 4 года назад

    Keep kicking butt Professor Leonard!!!

  • @guidofeliz8384
    @guidofeliz8384 4 года назад

    Wow! Almost one or two videos per day. I'm impressed.

  • @cleightthejw2202
    @cleightthejw2202 4 года назад

    Thanks for the lessons Prof Leonard

  • @somebody401
    @somebody401 Год назад

    Everything here makes sense! Can't thank you enough.

  • @vaughnmonkey
    @vaughnmonkey 4 года назад

    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?

  • @rosepierce9382
    @rosepierce9382 Год назад

    42:53 I want this printed on a tee.

  • @mikem9270
    @mikem9270 4 года назад +1

    Now you can all tell your friends that "You don't know your asymptote from a hole in the graph."

  • @andrewesquibel9614
    @andrewesquibel9614 3 года назад +2

    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
      @milandukic4080 3 года назад +1

      Did you find answer to this? I can't understand it either

    • @andrewesquibel9614
      @andrewesquibel9614 3 года назад +1

      @@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.

    • @andrewesquibel9614
      @andrewesquibel9614 3 года назад +2

      @@milandukic4080 For example, (x + 3/2) is not equivalent to (2x + 3). But 2(x + 3/2) is equivalent to (2x + 3).

    • @andrewesquibel9614
      @andrewesquibel9614 3 года назад +2

      @@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.

  • @Gavin_Gladiator975
    @Gavin_Gladiator975 Год назад

    What if the leading coefficient for the numerator is bigger than the denominators with a higher power
    Ex)
    (2x+2)/
    (X^2+1)

  • @zeeshan7372
    @zeeshan7372 2 года назад

    Damn good professor

  • @janoycresva276
    @janoycresva276 4 года назад

    Big Lenny is the Tom Platz of Math

  • @plamenyankov2182
    @plamenyankov2182 4 года назад

    Hi Professor Leonard, are you going to do a linear algebra course within the next year or so? Thanks!

  • @meat137
    @meat137 4 года назад

    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! :)

  • @saul123x
    @saul123x 4 года назад

    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

  • @bfonsecat
    @bfonsecat 3 года назад +1

    The hole point of a missing point 🥴👌🏻

  • @anynomouse
    @anynomouse 4 года назад +1

    How can l practice everything l have learned. I self learn so l don't follow a teacher and don't receive homeworks.

    • @user-bl9ir7xo4n
      @user-bl9ir7xo4n 3 года назад +1

      did you solve this? I'm having the same problem

    • @malekstudies0944
      @malekstudies0944 2 года назад

      @@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

  • @theaveragemegaguy
    @theaveragemegaguy 4 года назад

    I love you so much

  • @wasabikemosabe1773
    @wasabikemosabe1773 4 года назад

    Has anyone ever told you you look like a really buff Stephen Colbert?

  • @etudemath8052
    @etudemath8052 4 года назад

    Sir I am the biggest fan of your teaching method.
    I request you to start Linear algebra...please...

  • @MrBluemanworld
    @MrBluemanworld 4 года назад +1

    Offering knowledge for free....that's where it's at....yup Professor Leonard is getting laid.

  • @stircrazygenius8464
    @stircrazygenius8464 4 года назад +2

    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.