In this video, I soleved an inequality of the floor of a quadratic ceiling function. Yeah, it sounds confusing.
Пікірлер: 15
@happyhippo46643 ай бұрын
Chem Eng here. Took dozens of math classes in high school and college. Old man now. Never heard of floor and ceiling functions. Never stop learning, indeed.
@user-gf4eg4rm5r3 ай бұрын
This explanation is easy to understand❗️👏👏
@andreasjoseph1443 ай бұрын
Thank you sir,atleast now i understand better then before,🎉🎉 Be blessed sir
@WhiteGandalfs3 ай бұрын
Interesting to see how the curve plot translates into pure formula handling. While the curve plot is very simple and easy (and secure) to understand, the translation into formulas provides for automation with programming.
@JourneyThroughMath3 ай бұрын
When I solved, i dropped the floor first and then added 1. Is that okay, or will that not be true in all cases? It feels like it would be true.
@glgou46473 ай бұрын
clean new pfp!
@surendrakverma5553 ай бұрын
Thanks Sir 🙏
@JourneyThroughMath3 ай бұрын
I worked the solution to get the ceiling of x is between -1 and 2. But honestly Im not sure if more is necessary
@JourneyThroughMath3 ай бұрын
I see what I did wrong
@tura3613 ай бұрын
The easiest question solved by a 15 years old child in Turkey. Geography is destiny.
@suryamgangwal83153 ай бұрын
Wont k be equal to -2,0,2 ?becasue we taking the ceiling of 1.732
@m.h.64703 ай бұрын
No, we are talking about the ceiling of x, not the ceiling of √3.
@sadeqirfan55822 ай бұрын
Please take out that dramatic part after you say “let’s get into the video” that comes with a music. It is excruciating.
@m.h.64703 ай бұрын
Solution: ⌈x⌉² - 1 is already an integer, therefore the floor function can be ignored: -1 ≤ ⌈x⌉² - 1 ≤ 2 |+1 0 ≤ ⌈x⌉² ≤ 3 x is therefore a real number. The lower bound becomes redundant: ⌈x⌉² ≤ 3 Replacing ⌈x⌉ with (k + 1), with k being integer (k + 1)² ≤ 3 |√ |k + 1| ≤ √3 Substitute k + 1 with t case t ≥ 0: 0 ≤ t ≤ √3 only t = 0 and t = 1 satisfy this inequality, as t is an integer case t < 0: 0 < -t ≤ √3 |*-1 0 > t ≥ -√3 only t = -1 satisfy this inequality, as t is an integer t ∈ {-1, 0, 1} as t = k + 1, we can say that k ∈ {-2, -1, 0} Since x = k + d, with 0 < d ≤ 1, we can say that -2 < x ≤ 1 Side note: It is 0 < d ≤ 1 and not 0 ≤ d < 1, because we used ⌈x⌉ = k + 1.