Same here. Although I get the aversion to "easy step by step formulas" of some teachers I think some things are better taught with some sort of "fixed procedure" until you start getting the handle of it... great lesson.
@@Redeemed_Daughter yeah,I learnt the thing in just an 8 minutes video just imagine after wasting hours streaming useless videos that won't even explain what they are doing and why they are doing it
does anyone know why in the beginning we have to say "Given epsilon > 0" but not "delta > 0". Why cant we just "0 < |f(x)-L| < epsilon" just like delta?
I have followed you through my high school and now I am still relying on your videos in my first year of engineering you have amazing content keep up the good work.Thanks a lot Sir.
I really had a hard time with epsilon-delta in my first semester in engineering but it turns out it's just matter of practice(for linear and 2nd degree polynomials 😅). It would be great if BPRP could show us geometrically the epsilon Delta
Extremely concise, thoughtful, and thorough explanation of how to use the epsilon-delta definition effectively and smoothly. This was so much more help than the book I'm reading through for Calculus. Thank you so much! This is a life-saver for college-level Calculus.
But you might also set ε < 8 so you are sure that what BPRP wrote is clear. ( ͡° ͜ʖ ͡°) Also this is a joke, but still this would be without loss of generality (the statement for limits works ∀ε>0 if and only if it works ∀ε/ 0
I thought you were me for a second and I was going loopy watching videos I'd already seen. Never seen anyone else with a map of CMB radiation as a profile pic. :)
this might be the most useful video i've ever seen. somehow managed to gaslight me into thinking it was easy and simple and then it really became easy and simple thank you you are a magician
more examples: linear, square root, and quadratic 👉 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yC8Y50H6kw8.html 1/x and x^3 👉 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-7VSG9G6EXrU.html
@@aliaziz1145 we definitely had a couple sections in my calc 1 class that were dedicated to delta epsilon proofs. Technically optional but not as far as my teacher was concerned haha
For the second example where you said (@(8:27) root (2x+6) is always positive and thus {(2|x-5|) / (root(2x+6) + 4)} < (2|x-5|) / 4. Instead, could you have said the entire denominator (root(2x+6) + 4) is also positive and thus { (2|x-5|) / (root(2x+6) + 4) } < (2|x-5|). The result is that delta is equal to Epsilon/2 vs 2.epsilon. Is "Epsilon/2" an acceptable answer?
Thank you so much for this... I am trying to get a headstart on calc out of Stewarts Calculus and they really don't do a very good job of explaining in the text so you just got me dug out of a ditch trying to understand what to do with exponents.
I almost wish my university would've had more time to focus on the delta-epsilon proof. We never went over the notation used for the limit of the quadratic so thankfully I learned about it before moving on from being an undergrad.
Learned something new. This was a bit different from other vids as I could try the problems along with you. Really a great experience. Please do keep having more such alongside trial videos. BPRP Yay!
I’m not taking calc(not old enough yet to take it lol) but it was always difficult for me to wrap my head around quadratic epsilon delta proofs, it feels like this opened my 3rd eye
Glad it was helpful! This is the video 24 rigorous limit proofs (ultimate calculus tutorial) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-AfrnYS5S8VE.html
For the last problem, we could instead choose δ to be (sqrt(49 + 4ε)-7)/2, and it would be a less strict condition as min{1,ε/8} ≤ (sqrt(49 + 4ε)-7)/2 for all ε. If, say hypothetically, we had to pay according to how small we chose δ to be, then we wouldn't want to choose it any smaller than we actually need to. In that case, the more complicated expression would cost the least. In any case, it was a great video, as always!
Could you please solve this? Let lim n approaches to Infinity n(cube root of(n^3+6n^2+3n+2)+ square rootof (n^2-4n+2)-2n) = p/q where p and q are coprimes then the value of p+q is equal to ? Please make a video on this!
Thank you! Do you have explanations of delta epsilon proofs in other contexts than just a limit (such as limit of a sequence, uniform continuity, etc)?
It is so important to keep sharp with these proofs. In today’s world of “dumbing down” we are graduating students who, more or less are not able to think outside of the box. #alifetimeoflearning.
I wish I had these videos back in times i was taking calculus I class. However I succeed my Calculus I part 2 exam (mostly based on series and series of functions) thanks to your videos
So… the goal is to somehow relate epsilon to delta? Once you have done that you’ve already proven the limit? No matter how close you’re approaching the given value (delta) you can always find a certain corresponding function value (epsilon), which is exactly what a limit is meant to represent, you are never exactly landing at let’s say x=2 but you can get as close as you want to it, thus the limit will be that value.
Great video! I'm a bit confused when I was supposed to learn this though because I'm taking Calc 2 now and was never taught this in Calc 1 or 2 so I guess the teachers assumed it wasn't important or just didn't have time
@@angelmendez-rivera351 oh it's been a while..so one corresponds to x and the other to f(x) I take it? Epsilon for x and delta for f(x) or vice versa..
How could we just remove the sqrt(2x+6) part for the second example? And what are we really doing to justify that? Are we looking for the minimum value that specific term can take (which is 0)? Aka min{ sqrt(2x+6) } = 0?
By removing a NON NEGATIVE value from a POSITIVE SUM in the denominator, you're GUARANTEEING that you're making the denominator SMALLER, but you're also keeping it POSITIVE. That in turn guarantees that the whole value becomes bigger (try it on simple numbers like he did - 1/4 vs 1/(4+1)) Do notice that if the denominator was the product of two positive things and not sum, he couldn't have done that move so easily (if at all), Because he can't know if he'll be removing a number between 0 and 1, or a number larger than 1, so won't be able to guarantee that the denominator will actually become bigger, probably unless he plays with the delta requirement or something that I'm too lazy to think about. When adding / removing things in the inequality trip, you'll mainly want to pay attention to positive /negative values, values that you don't know if they're always positive or not, checking if values are a fraction or bigger than 1 ( matters when a product is included in the game).
Hello, thank you for this video, it is really helpful. I have a question in mind: In a new video, can you use the same method for the trigonometric and exponantial functions as well as a polynomial function which we cannot write as product of two or more polynomials? For instance as lim x->10 (x^2 -x+89). Because in the example showed in video, we reached x-2 easily so our assumption about delta was helpful. How are we going to do when it won't be like this? Thank you in advance and thank you for this amazing channel! Videos are not only helpful but also inspirational!
Thank you for this video! I could not figure out how to do the quadratics of these for the life of me. The answer key in the back of the book has the answer but no sufficient explanation. And the only other example I could find on RU-vid was of a quadratic the factored to a perfect square which comes out much nicer in these circumstances.
