Epsilon delta proofs 2 - Quadratic and cubic functions
ฝัง
- เผยแพร่เมื่อ 12 ก.ย. 2024
- In this video we show how to use the epsilon-delta definition to prove limits involving quadratic and cubic functions. We also define what it means for a function to be continuous (at a point and on R), as well as introduce the viewer to the triangle inequality and demonstrate its usefulness in proving limits. Three examples are presented in all, with the last of them being done in two different ways:
1. lim_(x to 3) x^2 = 9 proved at 0:50
2. Continuity introduced at 17:35; lim_(x to a) x^2 = a^2 proved at 19:50
3. lim_(x to a) x^3 = a^3 proved at 25:00
4. A second approach to lim_(x to a) x^3 = a^3 at 32:25
U explained the reasoning
|x+3| being < 7 using triangular inequality so well. It is commendable.Thank u so much
6:22
|x+3|
Thank you so much! I teach Calculus I have researched several videos on how to go about proving cubic functions and this is by far the most clear cut and concise explanation. Excellent work!
Thank You So Much for this video!! I intuitively calculated the value of delta using the Quadratic equation method, but most of the videos on TH-cam demonstrated the method where delta is stipulated to be less than or equal to 1. I was in a dilemma as to whether my proof was correct or not. Thanks for clearing all my doubts!
You are an amazing teacher!!
Thank you this video is really good 👍. Made me understand very well.
UFT really got the best profs ...
Best video online regarding epsilon delta proofs, thanks
Great video, thanks!
11:19
The reason for choosing whichever minimum between δ=1 & δ=ε/7?
Do we know which one of the two is larger? Apparently we do not know.
Is the reason for choosing the smaller is that the larger value between the two can throw the value of function out the ε window?
5:56
Why did u choose the upper bound for x+3?
U chose x+3
I got that delta = epsilon/3a^2+3a+1, is there one way for proof. This is for lim_(x to a) x^3 = a^3
Thank you!
not bad at all, and optimally it was very good :P
Wow
14:20 For degree n the optimal delta formula is (𝛿 + |a|)ⁿ = 𝜀 + |a|ⁿ.
However, as much as I would like to say this method is correct, its validity is not as simple as it seems.
Could it be somewhat "circular" because we did not yet prove that the nth-root function is defined and continuous?
How did u type power of something in iPhone TH-cam comments? Thanks
I comment from a computer, not an iPhone. I copied the symbols from other websites like Wikipedia et cetera.@@user-qj3rv2mo1b
Talk Nerdy to me