Proving existence of x-intercept in given domain (Bolzano's Theorem)

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  • Опубликовано: 7 янв 2025

Комментарии • 19

  • @SmithCS
    @SmithCS 6 лет назад +10

    I’m addicted to your videos. I love how you explain concepts that most students know, but don’t know why they are that way.

    • @joemama-js6hv
      @joemama-js6hv 6 лет назад

      a great example of a great teacher.

  • @martingeorgiev999
    @martingeorgiev999 Год назад +4

    "i drew it and there are no other roots" is not a proof

  • @billydimtsis
    @billydimtsis 4 года назад +2

    nice one
    but you can also say that this function (f(x)=x-e^(-x) is continues
    and f(0)=-10
    so f(0)*f(1)

    • @sakisroubas3237
      @sakisroubas3237 2 года назад

      xo cant be neither 0 or 1, so you have to lim and fnd an approximate number f.e f(a)

  • @bouteilledargile
    @bouteilledargile 6 лет назад

    It's it easy just to differentiate x-e^x to get 1+e^x and show that the derivative is always positive so it's a monotonic increasing function

  • @madhavstalks3925
    @madhavstalks3925 6 лет назад +6

    Sir please make the proper playlists of these videos as sometimes when I want to see some video I am not able to find that due to your large no. of videos.(>3.7K)s
    Hope an Early Reply....😊

  • @SANJEETkumar-yl5kt
    @SANJEETkumar-yl5kt 6 лет назад

    I have a very basic confusion --> in a function plot say t,f(t). The value at particular t, represents the value at that point 5th sec moment only or for whole 0 to 5sec amount of time?

    • @ethanp4050
      @ethanp4050 6 лет назад

      SANJEET kumar it represents the function at that particular point.

    • @SANJEETkumar-yl5kt
      @SANJEETkumar-yl5kt 6 лет назад

      Ethan Palinkas thank you

  • @valeriebustos9268
    @valeriebustos9268 6 лет назад +2

    Can you start doing calculus and proofs? I know it's a lot to ask since this is probably high school level. But I think a lot will find it really helpful to have a great teacher such as you explaining the basics for university calculus such as definitions of limits, continuity and mean value theorem.

  • @duckymomo7935
    @duckymomo7935 6 лет назад

    Bolzano Weistrass theorem?

    • @JohnM...
      @JohnM... 6 лет назад

      Mi Les another name for the video theorem is the intermediate value theorem. The Bolzano-Weierstrass theorem is to do with boundedness of sequences.

    • @duckymomo7935
      @duckymomo7935 6 лет назад

      John M g
      O okay thank you
      His terminology is a bit confusing

  • @doctorwhodj
    @doctorwhodj 6 лет назад

    Can you crop the white board a bit more please to fit my screen better. The top left corner overexposed a bit too. Thank you for the videos🤙😎

  • @saiphaneeshk.h.5482
    @saiphaneeshk.h.5482 6 лет назад +2

    Holy Father of Maths, It was the easiest way uve come across to solve a problem.
    Using the graph is the easiest method lol.
    I didn't understand at the end that how you said that the intersection point of the two curves lies from 0-1???
    Clearly it's greater than 0,but how less than 1???

    • @ethanp4050
      @ethanp4050 6 лет назад

      SAI PHANEESH it’s referring so the DOMAIN not RANGE (I.e. x coordinates)

    • @JohnM...
      @JohnM... 6 лет назад

      SAI PHANEESH he's looking for the " root", I.e. the x solution. ( it's about 0.56)

  • @JohnM...
    @JohnM... 6 лет назад

    Yup - graph the two. Estimate a value for the root, say 1/2, and apply Newton's method.