Real Analysis 4 | Theorem on Limits

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

This is part 4 of 64 videos and here we discuss the important limit theorems.

00:00 Intro
00:18 Limit of a sequence
01:16 Theorem on limits
03:48 Example
06:22 Outro

#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[PunmasterSTP]

Theorem on limits? More like “These are the clearest vids!” Thanks for amazingly simple and concise lectures!

[SoopaPop]

Your example at the end there has a technicality worth noting to people learning real analysis for the first time. Technically the approach is to rewrite a quotient 2 divergent sequences as a quotient of 2 convergent sequences instead. It is important to make it known to first time readers of this subject that the limit theorem may be used in the last step, after obtaining the two convergent sequences.

[JimmyBriggs]

Just joined the patreon! These are wonderful!

[flemingmontesaldazabal]

Super!!
What book do you recommend for real analysis?

[skillick]

In the case of the example would it also be okay to:
lim 2n^2 + 5n -1 / lim -5n^2 + n + 1
Then take L'Hopital's rule to get:
lim 4n + 5 / lim -10n + 1
Then say we can ignore the constant terms as n becomes infinitely large.
so we have:
lim 4n / lim -10n
So as n becomes infinitely large we can say the limit has a ratio of -2/5