¶ When we speak of a variable taking on different values, it is implied, although usually not expressly stated, that there is some law which governs the successive values that it assumes. For example, if say that x approaches zero as a limit, it may do so through the sequence of values (4) 1/10, 1/100, 1/1000, 1/10,000, . . . or through the sequence (5) 1/2, -1/4, 1/8, -1/16, 1/32, -1/64, . . . or, starting with 1, it may assume all positive values in the order of decreasing magnitude. Variables do not necessarily attain their limits; thus zero is a number of the sequence (4) or of (5); nevertheless the limit of each of these sequences is precisely zero. However in other instances a variable may take its limiting value. ¶ Occasionally the nature of the discussion may it limitations on the behavior of a variable. For example, if we have in mind log(x - 2) and wish to consider what happens when x → 2, we may wish to limit the manner of approach to values of x > 2, because, when x < 2, log(x - 2) is imaginary. If x is required to approach 2 through values greater than 2, the symbols used are x → 2+; similarly x → 2- means that x approaches 2 through values restricted to those less than 2.
This helped a ton! i wouldnt be able to solve a single epsilon delta question if i didn't watch this. now i feel like i can solve lol. at least i know what to look for. thanks a lot mate! would love to see more abstract algebra & advanced calculus proofs as well
My multi variable calculus professor said that the epsilon delta proof was too hard to prove there exists a limit for a multi variable function and we are just proving there does not exists a limit instead. Well I did a crash course and did a couple problems using the limit of epsilon delta proof on a single variable and here I am! I am just confused with you said that the absolute value of y times the absolute value of x cubed divided by x squared plus y to the fourth is less than or equal to the absolute value of y times x cubed divided by x squared? Nvrm I just realized that the bigger the denominator the smaller the value. Wow how funny how that helped me understand right now by typing it out haha. Thank you!
Sir , you’re amazing . If you could make a video on how to prove a set is open and closed , that’d be amazing . I know you somewhat made one , but I mean like say for all X in the reals ... prove x.a> c is closed etc
@@TheMathSorcerer you know what I was thinking, you should do some abstract algebra (groups, rings, ideals, fields) I think you have the talent to explain that just as well as you explain other topics.
what if I assume that y is not equal to zero and eliminate x^2 terms in the denominator? I have solved some problems by following your technique and I had contradictory relations when assuming x is not equal to zero and in the other case y is not equal to zero...please tell me
that's a key step, super important to know this! Ok so if you have say 1/(x + 2) , you can write 1/(x + 2) 0 in this case, because 1/(x + 2) is smaller than 1/x because x+2 is bigger than x. Remember whenever you have a fraction, it's smaller if the bottom is bigger. Another example: x^2y/(x^7 + y^6) 0 in this case(you don't want to divide by 0
Thanks for a great video! I have a question according limit in multivariable. Is it a way to show that a limit doesn't exist with epsilon-delta method? =)
I believe it is because he isn't diving by y. He had to do the case analysis, as the term |x³/x²| would not be defined for x=0. But y=0 is a "carried" option through his entire proof, or rather the only case it wouldn't be, is, if x=0 too.
you cannot explain it , you have to explain things in terms of proper and clear teorems, en checking the conditions of the teorems, not by intuition talking like whe have this and we have that , not good
merhaba , limit in prensibini anlamiyordum ben bu vidyoyu izledigimde. Limit in prensibini artik iyi cozdum, bu yuzden bu vidyo artik mantikli. Yapman gereken sey , butun leptoplari telefonlari kapatmak , odandaki isigi sondurmek ve izdivaca cekilip limit hakkinda dusunmek, ve sonra prensibi anlacaksin, selametle
ha bide kendine kahveli sut kaynat , biraz seker at, ic. Karanlikta ama , yatginda sonra dusun ama zihnini rahat birak, vidyoyu anlatanda bi insan , o anlayabiliyosa sende anlayabilirsin
¶ When we speak of a variable taking on different values, it is implied,
although usually not expressly stated, that there is some law which
governs the successive values that it assumes. For example, if say
that x approaches zero as a limit, it may do so through the sequence
of values
(4) 1/10, 1/100, 1/1000, 1/10,000, . . .
or through the sequence
(5) 1/2, -1/4, 1/8, -1/16, 1/32, -1/64, . . .
or, starting with 1, it may assume all positive values in the order of
decreasing magnitude. Variables do not necessarily attain their limits;
thus zero is a number of the sequence (4) or of (5); nevertheless
the limit of each of these sequences is precisely zero. However in
other instances a variable may take its limiting value.
¶ Occasionally the nature of the discussion may it limitations on the
behavior of a variable. For example, if we have in mind log(x - 2)
and wish to consider what happens when x → 2, we may wish to limit
the manner of approach to values of x > 2, because, when x < 2,
log(x - 2) is imaginary. If x is required to approach 2 through values
greater than 2, the symbols used are x → 2+; similarly x → 2- means
that x approaches 2 through values restricted to those less than 2.
You've helped me in almost every math class I have as a senior in undergrad. I keep finding gems on your channel. Much love
This helped a ton! i wouldnt be able to solve a single epsilon delta question if i didn't watch this. now i feel like i can solve lol. at least i know what to look for. thanks a lot mate! would love to see more abstract algebra & advanced calculus proofs as well
My multi variable calculus professor said that the epsilon delta proof was too hard to prove there exists a limit for a multi variable function and we are just proving there does not exists a limit instead. Well I did a crash course and did a couple problems using the limit of epsilon delta proof on a single variable and here I am! I am just confused with you said that the absolute value of y times the absolute value of x cubed divided by x squared plus y to the fourth is less than or equal to the absolute value of y times x cubed divided by x squared? Nvrm I just realized that the bigger the denominator the smaller the value. Wow how funny how that helped me understand right now by typing it out haha. Thank you!
Yeah I love when that happens! That is often the case, you type something out and it helps you clarify your thoughts and bam, it all clicks:)
5:04 how do you drop the Y to the fourth without consequence? What is the reasoning?
Sir , you’re amazing . If you could make a video on how to prove a set is open and closed , that’d be amazing . I know you somewhat made one , but I mean like say for all X in the reals ... prove x.a> c is closed etc
thank you professor. you are my one imaginary professor for this covid period :)
Hehe
Watching this after doing 14.2-14.6 in one day, with one eye open at 1am. Ty ty ty 😉 This is worth 2% extra credit on our 2nd exam tomorrow.
Nice!!!
That is a lot in one day too lol
you saved my life
Hehe glad it helped😄
thank you sir this example is very helpful.
U saved my ass, been struggling wit the hw for a while…
So all of a sudden you just decide to drop y^2 and you don't explaining why you did that and what's the reasoning behind all that?
I want to know the same
@@manish8911 mee too
As a computer scientist who literally sucks at maths, this video saved me thanks 😁
Haha awesome so glad it made sense😄
@@TheMathSorcerer you know what I was thinking, you should do some abstract algebra (groups, rings, ideals, fields) I think you have the talent to explain that just as well as you explain other topics.
Thank you! It helped me a lot but I still cannot solve a question about this topic. Could you please help me🥺
Great method!
Legend, thank you!
what if I assume that y is not equal to zero and eliminate x^2 terms in the denominator? I have solved some problems by following your technique and I had contradictory relations when assuming x is not equal to zero and in the other case y is not equal to zero...please tell me
I love how the channel name is sorcerer..but it's the photo of Gandalf the wizard🤣
hey sir you're amazing
would you solve this problem?
lim(x,y)tends to (1,1)(x^2+xy+y^2)=3 then prove using epsalon delta??
why were you able to drop the y^4?:)
that's a key step, super important to know this! Ok so if you have say 1/(x + 2) , you can write 1/(x + 2) 0 in this case, because 1/(x + 2) is smaller than 1/x because x+2 is bigger than x. Remember whenever you have a fraction, it's smaller if the bottom is bigger. Another example: x^2y/(x^7 + y^6) 0 in this case(you don't want to divide by 0
The Math Sorcerer thank you so much , that clears it up 😁
@@mialynch5086 Oh that's awesome! So happy that helped, this is such a USEFUL technique!!!
Good explanation
@@TheMathSorcerer LIFE-SAVER!!!!
You have really helped me during this whole pandemic 😞❤️
thank you!
You're welcome!
Thank you so muchhhh :")))))
You are welcome !
❤️
Thank you professor.
Can you please keep the screen white
Sure I can make some like that😀
Thank you very much professor
You didnt give us any reasoning to why you dropped the y^4
Yea bruhv ...if you've found out why please tell😢
So if |x| is
You could just let delta be = sqrt(eps)/2. Also observe that the epsilon-delta definition works just as fine with
Think about the definition of delta. 0
Thanks
Wonderful
Thanks for a great video!
I have a question according limit in multivariable. Is it a way to show that a limit doesn't exist with epsilon-delta method? =)
Actually there is, I should make a video on that specifically as I don't have any. I have a few for sequences but not limits.
That would be appreciated since I haven't found any video with examples of that. =)
@@TuananhNguyen-kl8ud exactly my doubt, ty
@@TheMathSorcerer Have you by chance uploaded it by now? I am scrolling down your vids But there are way too many :c
👍🏻Thanks
you are very welcome! I am happy this was helpful:)
Why do you not have to mention the case where y = 0?
I believe it is because he isn't diving by y. He had to do the case analysis, as the term |x³/x²| would not be defined for x=0. But y=0 is a "carried" option through his entire proof, or rather the only case it wouldn't be, is, if x=0 too.
awindwaker but what if y = 0, and you check for when x != 0. Just doing the same process but switching variables.
@@awindwaker4130 Thats very important!!!
Did u figured out why he didn't mention the case where y=0
Merci
why y should be different than 0
♥️
:)
you cannot explain it , you have to explain things in terms of proper and clear teorems, en checking the conditions of the teorems, not by intuition talking like whe have this and we have that , not good
Thank you someone understood my point we need certainty not we have this we have that
çok haklısın bu konu hakkında doğru düzgün video bulamıyorum bulduysan bana da söyler misin
merhaba , limit in prensibini anlamiyordum ben bu vidyoyu izledigimde. Limit in prensibini artik iyi cozdum, bu yuzden bu vidyo artik mantikli. Yapman gereken sey , butun leptoplari telefonlari kapatmak , odandaki isigi sondurmek ve izdivaca cekilip limit hakkinda dusunmek, ve sonra prensibi anlacaksin, selametle
ha bide kendine kahveli sut kaynat , biraz seker at, ic. Karanlikta ama , yatginda sonra dusun ama zihnini rahat birak, vidyoyu anlatanda bi insan , o anlayabiliyosa sende anlayabilirsin
❤