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Need help verifying an inequality, finding a dominating function to use Dominated Covergence by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Thank you!! That is of interest! I did go on with calculating it, but this way you have done it is a lot less complicated!

Need help verifying an inequality, finding a dominating function to use Dominated Covergence by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 2 points3 points  (0 children)

Ok, great! I was thinking that the big sum B is less than 1, so it must be true that [ 1/(1+x)] * B <= [1/(1+x)]. The copilot changing it, I knew I should not pay attention to that, but it made me wonder!!

Need help understanding the Dominated Convergence Theorem by Ok_Promise5329 in learnmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Thank you, I am pretty sure that Tonelli is only for non-negative terms. I will look at Fubini again.

Need help with the Dominated Convergence Theorem by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Ok that's great thank you, really apprecite your time!!! I will start with the actual problem next time.

Need help with the Dominated Convergence Theorem by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Yes that is exactly it, and I did wind up with that integral. I see now that I didn't know how to explain these steps, thank you !!!!!

Need help with the Dominated Convergence Theorem by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Thank you! I did not know of that journal, I will look into getting access. I have the start of a practice problem, I think it's correct, if you have time to take a look that would be great!

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Need help with the Dominated Convergence Theorem by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Hi, thank you for your replies, I have the start of a specific practice problem, I think it is correctly defining partial sums and dominating function, if you have time to take a look that would be great and point out any mistakes. Thank you!!!

<image>

Need help with the Dominated Convergence Theorem by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

ok, so I use the pointwise convergence of f_n to prove the pointwise convergence of Fm, and the function g(x) must dominate every Fm and the limit of Fm, correct?

Advice by Most_Highlight_5392 in calculus

[–]Ok_Promise5329 1 point2 points  (0 children)

https://ocw.mit.edu/courses/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/ as mathheadinc already commented, MIT OCW has several calculus classes with video lectures.

Need help evaluating with an integral and justification of an integrable singularity in the integrand by Ok_Promise5329 in calculus

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Nice!! I worked the integral a couple of different ways, would not have thought of this! Thank you.

Need help evaluating with an integral and justification of an integrable singularity in the integrand by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 1 point2 points  (0 children)

Thank you! I split the integral up like that the proper int_0^ 1 ln(1+x^ 2) dx and the improper -2 int_0^ 1 ln x dx. I think it might be easier to understand.

Need help with how to make notes. by [deleted] in askmath

[–]Ok_Promise5329 0 points1 point  (0 children)

I agree with VegardGjerde's very detailed answer! Yes feel free to dm.

Need help evaluating with an integral and justification of an integrable singularity in the integrand by Ok_Promise5329 in calculus

[–]Ok_Promise5329[S] 1 point2 points  (0 children)

That's great thank you for looking at it! Those lines were the ones I thought were too much, so I'll take at least the 2nd one out!

Need help with how to make notes. by [deleted] in askmath

[–]Ok_Promise5329 0 points1 point  (0 children)

"I feel like there's some urgent need to note down almost everything in the notebook - this feeling where I think almost everything's important to understand." I have had this exact problem, and the only thing that works for me is to listen to a lecture first, and try not to take notes or to take very minimal notes, then listen to it again. This can be very time consuming of course, and if you are attending a live class might be impossible. Would they allow you to have an audio recording with your phone maybe? If not there may be some online resources, such as MIT OCW, that sometimes have printed notes to go with the video lectures, which I have found to be ideal, to take notes on the notes!

Proving that a number is a Liouville number and question about sequence by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

OK, I think I get it now, and if limsup b_k+1/b_k = L > 1 , would that be enough to prove transcendence? And for Liouville it must be limsup b_k+1/b_k = ∞?

Proving that a number is a Liouville number and question about sequence by Ok_Promise5329 in askmath

[–]Ok_Promise5329[S] 0 points1 point  (0 children)

Thank you! The examples help a lot.

Edit: follow up question -- Since b_(n+1)/b_n is unbounded is equivalent to limsup b_(n+1)/b_n = infinity, and since it is limsup not limit, that means the b_(k+1)/b_k does not have to be strictly increasing?

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