The Derivative in Calculus Defined as a Limit - [1-2]

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  • เผยแพร่เมื่อ 2 ม.ค. 2025
  • More Lessons: www.MathAndScie...
    Twitter: / jasongibsonmath
    In this lesson, you will learn what the mathematical definition of a derivative is in calculus. The derivative is defined to be the slope of the line tangent to a function at a point. In order to do this, we find the slope of a line passing through two far away points, then slowing move these points closer together using the limit process. The derivative is then defined to be the slope of the line tangent to the function at a given point, and is calculated to be the slope of the line through two points, as the limit takes these two points to be infinitely close together.

ความคิดเห็น • 39

  • @khalilfuller4939
    @khalilfuller4939 9 หลายเดือนก่อน +5

    No jokes aside you are the truth. I even highly recommend to people that your videos is worth every penny

  • @V21IC
    @V21IC 11 หลายเดือนก่อน +2

    I think that I'm learning Calculus!
    I saw a feed on Facebook but it was dubios that I had to search for clear teaching on the subject!
    I think many teachers try to show how 'smart' they are instead of imparting knowledge to be understood by learners.
    I must say, that you're humble and teaches very well!
    Your style is like a breaking story that I've never heard in decades!

  • @wez3107
    @wez3107 4 หลายเดือนก่อน

    Simple, intuitive explanation of a derivative. No need to overcomplicate it.

  • @biffboffo
    @biffboffo ปีที่แล้ว +3

    I wish I had something like YT in high school in the 80s. I had a calculus teacher who wasn’t very good, and it would’ve helped me tremendously to hear the explanation from someone else.

    • @Rem91067
      @Rem91067 8 หลายเดือนก่อน

      Same here. My calculus instructor didn’t like to explain things; he just blew through it all and I couldn’t follow. I ended up dropping the class. Up until then, I had always done well in math. My failure to comprehend calculus really disheartened me and dashed any hope I had of majoring in the sciences.

  • @83jbbentley
    @83jbbentley 2 ปีที่แล้ว +11

    Calculus reflects many of the ongoing math problems of the time.
    -tangent line
    - area under curve
    It’s really one of the most amazing breakthroughs of modern man. Like the printing press. Think how costly book were? It’s like YT in a way. Imagine teachers like you who’s impact is so far stretching that most people don’t understand

  • @kwenda
    @kwenda ปีที่แล้ว +1

    All I can say is where were you all these years hahah. Going back to University and stumbled upon this and I can’t stop learning. Thank u.

  • @wthornton7346
    @wthornton7346 14 วันที่ผ่านมา

    Love the pay off at the end, with the proof of y = mx + c

  • @hemrajue3434
    @hemrajue3434 2 ปีที่แล้ว +10

    I think slope definition gives us slope between two discrete points whereas the limit definition of derivative gives us the slope at a point of a continuous curve.

    • @MathAndScience
      @MathAndScience  2 ปีที่แล้ว +4

      Very well said!

    • @V21IC
      @V21IC 11 หลายเดือนก่อน

      Couldn't agree more!
      Thanks!

    • @V21IC
      @V21IC 11 หลายเดือนก่อน

      Damn! I think you just nailed it!🎉🎉
      1. Slope(of a curve) - A straight line touching two points along a curve!
      Any two points in between may have a different slope.
      2. Limit - The point on the curve and from which a slope can be derived!
      Wow!
      Limit definition is one point along the curve WHERE a slope can be derived!
      So, when the line touches two points along the curve is a slope.
      A line touching one point is the limit from which a slope can be 'derived'!

  • @sameerpabreja8742
    @sameerpabreja8742 ปีที่แล้ว +2

    Thank you so much, you are a real exam life saver.

  • @tresajessygeorge210
    @tresajessygeorge210 8 หลายเดือนก่อน

    THANK YOU... SIR...!!!
    It is hard to remember... but understands the concept ...!!!
    THANKS AGAIN...!!!

  • @lipingma9016
    @lipingma9016 ปีที่แล้ว +1

    Well explained !

  • @MrWadmaths
    @MrWadmaths 2 ปีที่แล้ว +4

    Amazing 👏

  • @matthewgaydos8642
    @matthewgaydos8642 2 ปีที่แล้ว +1

    I appreciate all Your Videos!😊👊😊☕☕☕

  • @sergiomorales4302
    @sergiomorales4302 2 ปีที่แล้ว +1

    You’re my hero

  • @davemoney6713
    @davemoney6713 4 หลายเดือนก่อน

    Thanks. You cleared this up!

  • @wilkyclergeot9416
    @wilkyclergeot9416 2 ปีที่แล้ว +1

    Thank you so much incredible teach for everything!!!

  • @ashtesera6949
    @ashtesera6949 ปีที่แล้ว +1

    You are brilliant teacher.

  • @surajshukla5741
    @surajshukla5741 2 ปีที่แล้ว +1

    Thanks sir

  • @gemini22581
    @gemini22581 ปีที่แล้ว

    Why did u substitute x+h for x???

  • @drumtwo4seven
    @drumtwo4seven 2 ปีที่แล้ว +1

    Nice 👍

  • @yuusufliibaan1380
    @yuusufliibaan1380 2 ปีที่แล้ว +1

    Good lesson thank you ☺️💕

  • @augmentedman
    @augmentedman ปีที่แล้ว

    Thank you Spiderman

  • @kostaskostas2470
    @kostaskostas2470 10 หลายเดือนก่อน +2

    It’s a good video but your argument that teaching limits is ridiculous is unfortunate. Calculus is all about limits. Limit is the revolutionary idea that allows calculus to develop. It is sad and not good to see calculus as differentiation and integration and teach the rules.

  • @sammin5764
    @sammin5764 2 ปีที่แล้ว

    🌟🌟🌟🌷🌟🌟🌟

  • @tyrone3668
    @tyrone3668 7 หลายเดือนก่อน +1

    I hate math

  • @qualquan
    @qualquan 8 หลายเดือนก่อน

    Toooo long