Taking out the y^2 in the denominator, and inserting the x^2, is probably going to confuse people. The thing to remember is, one of the tricks in epsilon-delta is that you can change the expression so that it is reliably as large or larger. At that point you're doing epsilon-delta on a different expression, but because of squeeze proof logic, if that different expression satisfies epsilon-delta, so does the original. That trick is often used in conjunction with another trick: limiting delta to a narrow domain around the point in question. Sometimes the domain is absolutely arbitrary, in which case a value of 1 is common. Sometimes there is an extremum or singularity you want to avoid, in which case the size of the delta matters.
You calculated this limit originally using polar coordinates, and you can get an epsilon-delta proof that follows this. From the step with 3x²|y|/(x²+y²), you note that x² ≤ x²+y² and |y| ≤ √(x²+y²), so 3x²|y|/(x²+y²) ≤ 3(x²+y²)√(x²+y²)/(x²+y²) = 3√(x²+y²) < 3δ, and finish as in the video. So where the original calculation wrote x and y exactly using r and θ, here we estimate |x| and |y| using r alone.
@@yoshikagekira500 what do you mean by ‘how frequent’? It’s mathematical logic, you can do it with as many functions and points as you want, no limit (!).
This is a stepping stone for calc 3 bprp on youtube
He said under my comment under the past vid that he wants to keep BpRp calc 1-2 (if i understood correcly but you can check the last one.)
@@sebas31415 sure
@@sebas31415GD player. And you use the same cube as me lol
This man is saving careers with his work
2:58 bro locked in
Taking out the y^2 in the denominator, and inserting the x^2, is probably going to confuse people. The thing to remember is, one of the tricks in epsilon-delta is that you can change the expression so that it is reliably as large or larger. At that point you're doing epsilon-delta on a different expression, but because of squeeze proof logic, if that different expression satisfies epsilon-delta, so does the original.
That trick is often used in conjunction with another trick: limiting delta to a narrow domain around the point in question. Sometimes the domain is absolutely arbitrary, in which case a value of 1 is common. Sometimes there is an extremum or singularity you want to avoid, in which case the size of the delta matters.
Beautiful explanation. Thank you very much. Please do more vids on these limits
Thank you. Great teaching.
Please make a video about 30 proofs of these multivariable functions. It'd be so valuable ❤🙏
Agree
you're a lifesaver!! thanks alot
i would like to see you solve one or two of ramanujan's more complex equations
You calculated this limit originally using polar coordinates, and you can get an epsilon-delta proof that follows this. From the step with 3x²|y|/(x²+y²), you note that x² ≤ x²+y² and |y| ≤ √(x²+y²), so 3x²|y|/(x²+y²) ≤ 3(x²+y²)√(x²+y²)/(x²+y²) = 3√(x²+y²) < 3δ, and finish as in the video. So where the original calculation wrote x and y exactly using r and θ, here we estimate |x| and |y| using r alone.
If this is calculus basics, I'd hate to see advanced topics.😂
(x,y)----(0,0) for xy/(x+y^2) can you solve this problem. Thanks
interesting, i didn't even know that there was an epsilon delta proof for f(x, y) funcions
there are epsilon delta proofs for every single metric spaces
Well, there are multivariable limits, and everything must be able to be done rigourously to be valid. ε-δ is simply the way we make limits rigourous.
@@lambertwfunctiondo you have some videos to show how frequent are the ε-δ proofs ?
@@yoshikagekira500 what do you mean by ‘how frequent’? It’s mathematical logic, you can do it with as many functions and points as you want, no limit (!).
@@stephenbeck7222 in which domain of math we work with ε-δ ? Some exemples
why this video missing on this channel
why is this unlisted?
Please show us in the next video the second case where the limit does not exist 😊🙏
Oh I did that in the previous video.
@@bprpcalculusbasicsI mean epsilon-delta definition)
Can u pls specify how just finding the delta value proves its limit exists?
bro pls help me. If a = 7-4sqrt3, find sqrt(a) + 1/sqrt(a)
The answer is 4
He's right.
under the assomption x
e 0 y
e 0 x^2+y^2>=2|x||y| car help show |f(x,y)|->0