Epsilon Delta Continuity (Example 5): Absolute Value
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- Опубликовано: 7 фев 2025
- In this video, I use the epsilon-delta definition of continuity to show that f(x) = |x| is continuous. This is a must-see for every calculus lover, enjoy!
Continuity Playlist: • Limits and Continuity
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The doctor is in the house! Absolutely! 😃
Dr. Peyam to the rescue once again. Thanks so much🙏.
I love your voice
Love it! Why was it not necessary to do two cases, one for positive x and another for negative x? Is there a way to prove the limit when x goes to a of the absolute value by using epsilon delta? I've only seen it done by direct substitution and lateral limits... I know a continuous function HAS a limit, but how do we prove lim(x goes to a) of abs(x) = abs(a)? would this be equal to that? Sorry if the answer is obvious, it seems easy but epsilon delta proofs just confuse me...
Do you have any tips for a new grad student when it comes to doing good research??? Any help very much appreciated Dr Peyam.
Cry a lot
@@drpeyam lolol I have a feeling I might just do that.
what is its first and second derivatives
Dr Peyam, would you do a video series for tensor/Ricci calculus? I am going to be taking general relativity course and I would love to get some background on tensors. Thank you 😊
Oh no 💀
@@drpeyam haha yeah it's not gonna be fun but I gotta take it 😅