Epsilon delta limit (Example 4): Limits at infinity

This part of the epsilon-delta series covers limits at infinity. You can find Examples 1 and 2 on blackpenredpen's channel, and Example 3 on my channel. Enjoy!

Note: I realized after the fact that this limit may be a bit too simple, but if you want to prove that the limit of f at infinity is L, you do the same argument as in the video, except with |f(x) - L| instead of just |f(x)|.

[dripminic]

you can tell this guy really loves his job

[patrickalava]

Dr. Peyam: I am a maths teacher and I hope I can bring even half the joy you show in these videos to my own classes. You inspire me. Thank you.

[SavageKingsMobileThrone]

The most positive teacher I have ever seen, come teach at my school, I beg WE NEED

[Andygg]

I am beyond bummed out that I didn’t discover this channel until after I graduated from undergrad. I would have been a much happier and successful student. Thank you for the content!!

[IsaacAIm]

I have been trying to understand this formal definition of limit concept. you made it so easy. Thank you

[saumitragautam]

You are a great man doctor. May you prosper and be blessed by God himself. Thank you so much.

[gnikola]

I will forever believe that these proofs are absolutely trivial, although that's not a bad thing, it just confirmes that the idea of the limit is as intuitive as it can get. So I have fixed feelings about them!!

[adoeadeer]

omggg i finally understand. in my calc class my teacher used uppercase D and E to illustrate N which confused me so much bcuz i didnt understand how delta and epsilon connected to them (specifically, why different variables were needed) THANK U SO MUCHHHH 😍😍😍😍

[priyasah]

Thank u so much sir 🙏....your explanation made it very interesting and easy👍

[WritersDigest-bf]

Dr. Payem you are outstanding and explained very well, thank you. Could u also use graphs of the function and show epsilon, delta, M and N on it to make it more visual.
Thank u

[aubrey]

I think the reason people have trouble with these problems is the proofs are circular, sort of like circular reasoning based on the definition.
I went to ProfRob on YouTube and he explained what was going on along the way in a couple simple examples.

[unsightedmath]

I didn't want this solution but my question was so related to this one. Thank you so much. And I must say be happy always like this :)

[vimbainashemuchuweni]

may the dear Lord bless you sir you made this topic so easy ah

[pranshisharma]

Ohh wait....I was studying something 😍😇😇😇....Just find your channel .... Sir! You was so awesome watch more as required 😇😇

[grahamquasebarth]

in the beginning would you not write x>sqrt of 1/epsilon rather than x>1/sqrt of epsilon or do I need to brush up on my algebra

[marcello]

Why this definition asks for all Epsilon greater than zero. If Epsilon is the rate of variation cannot be negative or am I wrong?

[Gaelrenaultdu]

Hello, i'm confused. I understand your demo, but, don't you have to start your proof from |x - infinite| > delta (or N) implies |1/x²| < epsilon ? I don't understand how you get rid of the infinite in the absolute value.

[americoaraya]

Dr. Peyam: Please proof Lim (x-->0) e^X=1 with epsilon-delta.

[weerman]

I really like your content... and your voice ;)

[derejeliknaw]

Prove that the lim(x/x^2+1)=0 at x goes to negative infinity please you answer it by epsilon delta definition