Basically, because 1/4 is the one-half the distance between the two possible function values (i.e., half of the distance between 1/2 and 1). We could have chosen any number for epsilon as long as 0 < epsilon < 1/4.
@praneelbhatnagar233310 күн бұрын
@@garytiner508 hey thank you for your reply. I don't understand why we pick an epsilon between 0 and 1/4 whats the rule for picking and trick
@tyleroliveira266517 күн бұрын
Loved the spline series ❤
@garytiner50813 күн бұрын
Thanks! 🙂
@Loots1Ай бұрын
awesome professor
@garytiner50813 күн бұрын
Thanks a million! 🙂
@AK47_4142 ай бұрын
4:11
@Stefabro2 ай бұрын
great video series!
@garytiner5082 ай бұрын
Thank you very much! And best of luck to you....
@ChristianMarsh-o5z2 ай бұрын
Unfortunately I am just going to copy your work onto my homework but fortunately I fully understand the entire proof. Thank you for explaining so well.
@garytiner5082 ай бұрын
Thanks for the message and your kind words! Best of luck in your class! 🙂
@loopwithyourfriends5 ай бұрын
super helpful series, thank you so much!
@ludwigvanbeethoven39708 ай бұрын
these videos have been incredibly helpful
@yiokreverso8 ай бұрын
If I have a more complex function, that F(x1) and F(x2)aren't numbers, like "lim x - > 2 of g(x) = { x^(2) if 0<x<2 , x+3 if x ≥ 2} isn't 4 " What can I do to resolve this??
@garytiner50813 күн бұрын
Sorry for incredibly slow reply. So the limit doesn't exist at x=2. Use epsilon =1/2 (or anything between 0 and 1/2). This is because 1/2 is one-half of the distance between lim x->2- f(x) = 4, and lim x->2+ f(x)=5. Then basically just follow my example.
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❤🔥🔥
@Hailee12310 ай бұрын
Thank you
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what a goat
@TaharProd Жыл бұрын
thanks a lot
@TaharProd Жыл бұрын
this is awesome
@RishitSrivastava007 Жыл бұрын
Shouldnt S have f(a)+f(b)?
@thatsme6998 Жыл бұрын
thank you gary super helpfull
@amritasarki5417 Жыл бұрын
I love you😊
@justinwilliam5693 Жыл бұрын
Thank you for explaining this. Very helpful, unfortunately my professor did not take the time to explain this despite giving homework on it. The book skips over a lot of steps and background info as well.
@sadececansu9 Жыл бұрын
Thanks a lot for this clear explanation😇😇😁
@Rezhna_A Жыл бұрын
thanks
@kavinkumart1276 Жыл бұрын
For this sum for 3 point rule what answer sir??
@ashenafidejene95122 жыл бұрын
great work , it is simple and clear
@garytiner5082 жыл бұрын
Thank you for your nice comment!
@BalaAso2912 жыл бұрын
Nice lecture
@garytiner5082 жыл бұрын
Thank you, Bala!
@jameyatesmauriat61162 жыл бұрын
Hi, thank you for your explanation. I really struggle to understand this analysis, are there anything that makes me understand it deeply?
@karenwillert63503 жыл бұрын
You just said everything I needed to hear so simply and succinctly--Thank you!
@udithweerasinghe64023 жыл бұрын
🤩
@jayjoshi34203 жыл бұрын
thank you
@algorithmo1343 жыл бұрын
Sir can you make inverse function thereoem
@slandrix52403 жыл бұрын
One question, how do you know what epsilon to pick? Is it just for convenience?
@jacobguerreso6753 жыл бұрын
Same question. Everything else makes perfect sense. Trying understand why epsilon equals greater than |f(x1)-L| wouldn’t work
@jacobbarats14933 жыл бұрын
Pretend that you didn't know it was 1/2 at the beginning. We just need to make the formula work for some epsilon, so at the end when we see that |...| + |...| > 1 when know that one of those terms is greater than 1/2 which we then let be the epsilon
@jesusdanielmiguelcova23602 жыл бұрын
Same question everything else is perfect
@gustavstreicher48673 ай бұрын
The size of the jump discontinuity is 1/2. The halfway point between those two is your best average guess of what the limit could have been if it existed. So, the distance between that best guess and either of the actual values on the disconnected curves in the function is 1/4. Like others stated here, you could leave your choice of epsilon to the end. You just need to find a single choice of epsilon for which the rest is true to disprove the limit. So, choose whichever makes that the case for what you've worked out despite it.
@adesina13 жыл бұрын
Thanks sir
@360mathematics63 жыл бұрын
Very nice explanation
@soheil92553 жыл бұрын
That was great . Thanks a lot .
@NotDead100083 жыл бұрын
What is S?
@garytiner5083 жыл бұрын
It is the area of a collection of trapezoids that (together) "resemble" the area under the graph of f.
@anuj88554 жыл бұрын
Thanks a lot sir you clear my very deep doubt 🙏🙏🙏🙏🙏🙏
@filiperodrigues14524 жыл бұрын
Thanks for making your class videos public! It helped me for my Uni class. Cheers from Canada!
@garytiner5084 жыл бұрын
Cheers, and no problem at all. Thanks for the nice comment, Filipe!
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@micahjack35994 жыл бұрын
thanks for making this video man
@garytiner5084 жыл бұрын
Thank you for watching! I just subscribed to you... Blessings to you, and your family.
@upfront_silver01364 жыл бұрын
Hi Gary thx for the math
@garytiner5084 жыл бұрын
Any time! Thanks for the comment, James!
@upfront_silver01364 жыл бұрын
No problem
@mahajawad40414 жыл бұрын
it is very clear, thank you
@mahajawad40414 жыл бұрын
thank you
@garytiner5084 жыл бұрын
:-)
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@zaytoonalkhatoony20284 жыл бұрын
Thank you so much for the video I know it might be strange but your videos really benefit me and my friends we hope you continue and it seems like you are following your passion therefore i want to say that i consider my self your student from the United arab emirates we hope you continue and never stop because remember you never know who you might help and how many future engeneries or mathematicians benefit from your videos and you may be a reason that our world change and evolve.
@garytiner5084 жыл бұрын
Well, thank you, Zaytoon. I'm very happy that you benefit from my videos. Thanks for your encouragement!