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Limits, But They Keep Getting Harder! 

Mathematics Lifeline
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30 окт 2024

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Комментарии : 29   
@swenji9113
@swenji9113 5 месяцев назад
That's funny how in France we don't teach L'hospital rule (i learned about it on internet after i got my PhD in maths for example) because we believe it doesn't help students understand what they do, while it's so commonly used as one of the primary calculus tools elsewhere
@Mathematics-Lifeline
@Mathematics-Lifeline 5 месяцев назад
Yes, I agree. L’hospital is so useful, but not for students who are new to limits
@swenji9113
@swenji9113 5 месяцев назад
@@Mathematics-Lifeline As a super fast calculus trick it's very strong tho. I'm surprised I didn't learn it earlier
@shaguftakhizar7612
@shaguftakhizar7612 5 месяцев назад
I suggest tou watch 3B1B's video on limits
@vbprogrammer95
@vbprogrammer95 5 месяцев назад
In Italy they teach it and then strongly advise against using it, and if you use it in a way that it causes circular reasoning (i.e. trying to prove something with L'Hopital that was used to prove L'Hopital itself) they will often not accept it
@Danaelivs
@Danaelivs 5 месяцев назад
@@swenji9113man, I used the L’Hopital on almost everything and it was sooo much easier man
@vbprogrammer95
@vbprogrammer95 5 месяцев назад
Once you learn that you can divide by the highest degree term, you also learn that you can just consider that. For example for limit 10 (lim x->inf sqrt(x^2-9)/(2x-6)) you just take sqrt(x^2) on the top and 2x on the bottom, and simplify that to |x|/2x. Now since x approaches positive infinity both |x| and 2x will be positive, so we can just ignore the absolute value and write x/2x = 1/2. That's how they teach it in Italy anyway, IDK about the rest of the world
@semihdemir6104
@semihdemir6104 5 месяцев назад
For 9 pull the to the seventh power outside of the limit which is possible bc the function is continuous. The limit inside is then actually defined as e so it will be e^7 as a result
@Mathematics-Lifeline
@Mathematics-Lifeline 5 месяцев назад
I like this approach, the only thing to consider is that we can’t say that the limit inside is defined as e. It does end up being equal to e, but that is not how e is defined. It is defined as (1+1/x)^x which is different. To do this method, we would still have to do the limit inside like I did in the video.
@adriengrenier8902
@adriengrenier8902 5 месяцев назад
for level 9, split it into left and right limits then substitute x=1/t for t-> ±infinity to recover usual exponential limit.
@cluborronn
@cluborronn 5 месяцев назад
Level 10 is way easier if you just consider that x^2-9 approximates x^2 and 2x-6 approximates 2x at large numbers. It simplifies to sqrt(x^2)/2x which is just 1/2
@Mathematics-Lifeline
@Mathematics-Lifeline 5 месяцев назад
Yeah, I agree. The reason that I put it as level 10 was simply because the systematic way to do it is tricky. It probably should’ve been level 7 or 8
@bakashiro
@bakashiro 5 месяцев назад
9 is harder than 10 😂
@Danaelivs
@Danaelivs 5 месяцев назад
True 100%
@katelynn_white
@katelynn_white 5 месяцев назад
Love love love this video! 🙀😻
@strikercool911
@strikercool911 5 месяцев назад
limits of polynomial fonctions are all around easy no matter the difficulty
@nddkhoa
@nddkhoa 5 месяцев назад
I'm here looking for direct/inverse limits
@swampdonkeyd
@swampdonkeyd 5 месяцев назад
😡me when the limit is level 10
@television-channel
@television-channel 5 месяцев назад
why no 2,3 dim integrals and lims:(
@JohnPasay
@JohnPasay 5 месяцев назад
Where is the one-sided limit method?
@suspended3785
@suspended3785 5 месяцев назад
I solved the 10th one orally in 3 seconds.
@dragonizeyt
@dragonizeyt 5 месяцев назад
How? Tell me..
@rithvikarun7112
@rithvikarun7112 5 месяцев назад
Ong this is basic
@mrozan3578
@mrozan3578 5 месяцев назад
​​@@dragonizeyta and b doesn't matter if we're taking the limit to infinity/ so it's just limit of |x|/2x and |x| = x if x is positive so it's just limit of x/2x. No need to complicate it like in the video
@Mathematics-Lifeline
@Mathematics-Lifeline 5 месяцев назад
In my experience, you need to show work like I did in this video. I agree that you can check and see the answer immediately and I even mention that in the video. However, just writing down the answer will often give you no credit, so it is important to go through this question the systematic way so that students can understand
@suspended3785
@suspended3785 5 месяцев назад
You can ignore -9 and -6 as they are insignificant as x goes to infinity. That leaves us with √x²/2x which is 1/2.
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