Establishing the limit of a rational function using epsilon-N

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  • เผยแพร่เมื่อ 18 พ.ย. 2024

ความคิดเห็น • 24

  • @SumbaSlice
    @SumbaSlice 3 ปีที่แล้ว +6

    This is hands down the best explanation I ever saw

  • @krisretro
    @krisretro 2 หลายเดือนก่อน

    This was a really good explanation. It solidified my understanding of limits of a sequence. Thank you very much

  • @hasnathjahan4604
    @hasnathjahan4604 3 ปีที่แล้ว +1

    Wow.. I can go to sleep now.. It helped my assignment.

  • @dylanico887
    @dylanico887 ปีที่แล้ว

    How can we know for sure that 19/9n < e? is it not a case where 19/9n is greater than |an-l|, which means it could be greater than e?

  • @brianchoi2944
    @brianchoi2944 4 ปีที่แล้ว +1

    Big help!!!

  • @liamobrien2596
    @liamobrien2596 3 ปีที่แล้ว

    omg thank you so much

  • @Maka8295
    @Maka8295 6 ปีที่แล้ว

    For the final step when you plugged in your N and simplified to epsilon, what do you do if your N doesn't simplify down to just epsilon? I have a constant term in my N that I can't get rid of.

    • @joshuahelston5379
      @joshuahelston5379  6 ปีที่แล้ว +2

      OreoMan, can you put ignore the constant? Remember, these are inequalities, so you can choose N to be larger to ensure you are less than epsilon. If the constant cannot be ignored, can you bound it somehow? This is what I typically try to do.

    • @Maka8295
      @Maka8295 6 ปีที่แล้ว +1

      Thanks for the quick reply, In my case the constant was actually the limit itself. I had 5/3 + 3/(3epsilon - 5).

    • @joshuahelston5379
      @joshuahelston5379  6 ปีที่แล้ว +1

      OreoMan I see, so your issue was that you are getting (essentially) 1/epsilon needs to be zero right? That is a bit strange, what was the limit you were trying to establish?

    • @Maka8295
      @Maka8295 6 ปีที่แล้ว +1

      very similar to the question you used as an example. I needed to show that (5n^2 +4)/(3n^2 + n +1) is convergent to 5/3. The thing I posted just before is my N

    • @joshuahelston5379
      @joshuahelston5379  6 ปีที่แล้ว +2

      OreoMan , I am getting a different possible N for yours, if you want. No fancy bounding needed. Try N=\sqrt((7\epsilon-3)/9) if I am not mistaken. See if you can find how I got that (assuming I did not make an error!!!)

  • @zhengbozhou5534
    @zhengbozhou5534 7 ปีที่แล้ว +1

    why you delete the absolute sign directly?

    • @joshuahelston5379
      @joshuahelston5379  7 ปีที่แล้ว

      Clement Zhou since n is a natural number, the absolute value was not necessary as I moved beyond that point, since I knew the expression would be positive.

  • @georgeanton302
    @georgeanton302 5 ปีที่แล้ว

    Hi! Thank you for the video; question... at around 3:40, we claim $n > 19/9e$. Thus is it necessary to "choose N > 19/9e" or can we just set $N = 19/9e$ since $n > N$ by implication.

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      @daxtonsamir9583 3 ปีที่แล้ว

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    • @jonasalexis4296
      @jonasalexis4296 3 ปีที่แล้ว

      @Daxton Samir instablaster =)

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      @daxtonsamir9583 3 ปีที่แล้ว

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    • @daxtonsamir9583
      @daxtonsamir9583 3 ปีที่แล้ว

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    • @jonasalexis4296
      @jonasalexis4296 3 ปีที่แล้ว

      @Daxton Samir glad I could help :D

  • @satibomofficial5200
    @satibomofficial5200 4 ปีที่แล้ว

    Sir i need help show That the limit of the sequence where Sn = 2n/n+4 is 2

    • @satibomofficial5200
      @satibomofficial5200 3 ปีที่แล้ว

      @Forrest Raul bots this is not Instagram related vdo ....