Thank you for this. As a freshman maths major my real analysis professor is extremely confusing. This video was much more clear even tho im not native English speaker.
I'm watching this video at the end of 2023, let's hope someone will respond, in the first step of the proof, you have chosen N > 1/sqrt(ε), meanwhile I noticed that our professor, usually says that we need to put a condition on n at the beginning and then after proving that limit by definition, he uses the A.P to get that condition and finishes the proof, I'm kinda confused, also if I were asked to determine a limit of a sequence and prove it, is it correct just to calculate it as we used to do in high school for example lim 1/x = 0 and then prove it?
yeah you would have to break it up and rewrite it maybe, i'd have to write it all down but you would have, assuming I factored correctly here, |(3n -1)/((2)(n + 1)(2n - 3))| = 3, tricky I know, then from there you have |3n - 1|/(2n(n + 1)) and then break it up using the triangle inequality the idea is if you have like , 1/(2n - 3) you can do, 1/(2n - 3) = 3, so that's 1/(2n - 3) = 3 super clever/super useful technique, hope this helps:)
What if you had something like "n+1" in the numerator? You would then want to make the numerator bigger, right? And how? I have the problem 2n + 1 / 3n^2 + 2 I can make the denominator smaller by making it 3n^2, but I don't know what to do after that.
@@TheMathSorcerer Could you do instead 2n + 1 / 3n^2 + 2 < 2n + 1 / 3n^2 < 2n + n / 3n^2 < 1/n, then choose n to be any natural number greater than 1 / epsilon ?
Thank you for this. As a freshman maths major my real analysis professor is extremely confusing. This video was much more clear even tho im not native English speaker.
You're very welcome!
Hnn.... So "Batchelor of Science in mathematics " is " maths major" there.... The syllabus is same too i guess btw That's what it's called here.
Fellow math major here with a hella confusing professor
Hi there,
at 2:14 why are you comparing 1/(n^2 + 4) with 1/(n^2) ?
Thanks in advance.
it’s the same kind of function but bigger
Umm I have a small doubt
sm1 willing to clarify ?
the doubt is that 1/n2+4
Why did you replace n^2 + 4 with n^2???
Can someone help me with that question:
How to prove it by the defination of limit ?
lim n->infinty 1/2^n =0 ?
I'm watching this video at the end of 2023, let's hope someone will respond, in the first step of the proof, you have chosen N > 1/sqrt(ε), meanwhile I noticed that our professor, usually says that we need to put a condition on n at the beginning and then after proving that limit by definition, he uses the A.P to get that condition and finishes the proof, I'm kinda confused, also if I were asked to determine a limit of a sequence and prove it, is it correct just to calculate it as we used to do in high school for example lim 1/x = 0 and then prove it?
What happens when the denominator isnt always positive? For example in this 3n-1/4n^2-2n-6??
yeah you would have to break it up and rewrite it maybe, i'd have to write it all down but you would have, assuming I factored correctly here, |(3n -1)/((2)(n + 1)(2n - 3))| = 3, tricky I know, then from there you have
|3n - 1|/(2n(n + 1)) and then break it up using the triangle inequality
the idea is if you have like , 1/(2n - 3) you can do,
1/(2n - 3) = 3, so that's 1/(2n - 3) = 3
super clever/super useful technique, hope this helps:)
@@TheMathSorcerer That's a really cool trick to create a valid inequality with a single "n" term.
What if you had something like "n+1" in the numerator? You would then want to make the numerator bigger, right? And how?
I have the problem 2n + 1 / 3n^2 + 2
I can make the denominator smaller by making it 3n^2, but I don't know what to do after that.
write it as 2n/(3n^2 + 2) + 1/(3n^2 + 2)
@@TheMathSorcerer Thanks for the quick reply! That does help!
awesome!
@@TheMathSorcerer Could you do instead 2n + 1 / 3n^2 + 2 < 2n + 1 / 3n^2 < 2n + n / 3n^2 < 1/n, then choose n to be any natural number greater than 1 / epsilon ?
Thanks a lot !
You are very welcome! I am so glad this helped someone:)
What about finding the N in epsilon
n / n^2 + 1
did you find N for this problem? I am currently struggling with this rn huhu
wait ikaw man diay ni sir ahahahaha. late nako nakita imo name
High quality video
Thanks ❤️
thank youiu