Limits by rationalizing | Limits and continuity | AP Calculus AB | Khan Academy

Поделиться
HTML-код
  • Опубликовано: 31 янв 2025

Комментарии • 35

  • @TirthPatel7923
    @TirthPatel7923 4 года назад +8

    Thank you so much, I have a test tomorrow and this helped me out with 3 problems on the study guide. Thanks again...

  • @alexl035
    @alexl035 7 лет назад +19

    8:14 minus 1 thats 3 quick maths

  • @annabanana5426
    @annabanana5426 4 года назад +5

    Omg this is super helpful!! Thank you so much!!

  • @usernoneofyourbusiness
    @usernoneofyourbusiness 2 года назад +10

    “So hopefully this graph helps you a little bit… err.. or if it confuses you, ignore it-“ *_ENDS VIDEO_*

  • @datascience_azamat
    @datascience_azamat 3 года назад +3

    Thank you! Explanation is just wow

  • @balenaraz6174
    @balenaraz6174 4 года назад +5

    Thanks a lot it was very helpful ❤️

  • @thanaa6401
    @thanaa6401 8 месяцев назад +1

    Bro nailed it

  • @ChristianGerardPBerou
    @ChristianGerardPBerou Год назад +1

    this will definitely help me on Wednesday's test

  • @jairoselin5119
    @jairoselin5119 4 года назад +4

    Nice explanation sir.Sir f(x) would have the same graph as g(x) except it wouldn't have the gap means f(x) is defined at the point but f(x) is also not defined at -1 Am I right?

    • @totoblox4242
      @totoblox4242 Год назад +2

      Ikr, what’s the whole point of a new function f(x) when u could just substitute -1 in g(x) directly and get the solution

  • @saylubarry6848
    @saylubarry6848 Год назад +1

    Great job 👏

  • @CuriousFear
    @CuriousFear 8 лет назад +3

    very informative

  • @green_quadrix
    @green_quadrix 3 года назад +1

    Woah that last part made it click! Thanks

  • @frantzlouislouicin6282
    @frantzlouislouicin6282 4 года назад +1

    Thank you so much

  • @Ny_babs
    @Ny_babs 7 лет назад +6

    Isn't also x < -5 the value of the square root not defined? Or at least graph-able?

  • @lenamolobi8182
    @lenamolobi8182 6 месяцев назад +1

    please try to not skip steps

  • @dawsonspratt754
    @dawsonspratt754 Год назад

    At 3:46, why do you have to use +2 instead of using -2?

  • @s10ihd27
    @s10ihd27 8 лет назад +1

    nice video

  • @cmpatel92
    @cmpatel92 7 лет назад +5

    why do we only consider the principle root of 4 at 8:10 ?

    • @Cashman9111
      @Cashman9111 6 лет назад +2

      cuz g(x) is function

    • @vasukumar5727
      @vasukumar5727 3 года назад

      and so that g(x) could only have 1 output at a given point.
      by the definition of functions.

  • @michaelwright8576
    @michaelwright8576 4 года назад +1

    why do you say that you cant use g(x) to find x->-1 when it is the same function as f(x). The way you described that is a little confusing

    • @mohammedyunus9188
      @mohammedyunus9188 4 года назад

      The function g(x) wasn't defined when x approaches -1 but f(x) was. So for people to get understanding of what is happening with g(x), he conceived the idea of f(x) when x approaches -1.

    • @Supersilvershogun
      @Supersilvershogun 9 месяцев назад +1

      Evaluating a limit at a particular value, requires that the function should be continuous at that value, because the limit at that value would be equal the value of the function for that x value.
      When the original function g(x) was rationalised, it wasn't equivalent to the original function until the constraint of x != 1 was explicitly stated.
      The thing is, normally, the function is continuous at the value of -1. So, to actively calculate the limit at -1, an *equivalent function f(x) had to be defined, with the constraint of g(x) removed.
      Because they are equivalent, the limit of f(x) = g(x).

  • @notcanisha
    @notcanisha 2 года назад

    "if it confuses you ignore it", that was the plan lol

  • @hemat6796
    @hemat6796 9 месяцев назад

    My spider senses say I don't understand it

  • @stradplayer90
    @stradplayer90 8 лет назад +1

    Hella clever

  • @tariq1587
    @tariq1587 6 лет назад

    Hi

  • @BilboStabbins
    @BilboStabbins 2 года назад +1

    even after studying I failed 💀, time to work ff 🍔

  • @sam1815
    @sam1815 3 года назад

    the answer in the end is completely wrong. because u plugged in positive 1 instead of -1 which wouldve resulted in a non real number.

  • @pyroboi5291
    @pyroboi5291 2 года назад

    I hate rationalizing man im not that good at math😢

    • @pyroboi5291
      @pyroboi5291 2 года назад +2

      But i want to be better