Відео

You are totally right. I dropped the negative off on the second half of the first integral. It will need a revision.

Yes it does. You are dead on. Looks like this one needs a revision.

A function can be bigO of a potentially infinite number of functions, as long as the g(x) we select grows faster than our function after a certain value. If you look at the graphs for the two functions, y=x and y=(log(x))^2 and you will see that if x is greater than 1, y=x grows at a much faster rate.

Thank you!

Got it, I will see if I can get a revision in this weekend. Thank you!

Glad it helped!

This is true because at the end of the day, this kind of proving simply requires some algebra ability and an understanding of what the members of the domain look like.

You are welcome!

Thank you, I and my students really appreciate all the great tools that people have created. Eventually I hope to pay it forward and create some great things for other teachers to use.

And specifically, thank you!

Sameer, if you put the bars in the first two slots, you will have a bowl with 5 pears, no oranges, and no apples. At the bottom of the question, it says there are 5 of each type of fruit. So there should be five pears. Let me know if you have a follow up.

Shiny_apricot, I am glad that it helped.

I am not sure about the question, but if I understand you right: I use the theorem to evaluate the limits in this video and I think for most purposes this actually is the quickest and most effective way of finding the limits of vector-valued functions. So I use the theorem one for the limits problems. I think I glossed over the limit definition because I didn't want to go into evaluating distance(the two bars on either side of definition of the limit) and all of the machinery of calculating a magnitude when the theorem really was more intuitive and connected better to early ideas of single-variable calculus. So in short, the theorem is actually how we would find limits. I hoped that helped. Let me know if you have a follow up.

@@georgefsweeney Thanks!

Wonderful Bouazabachir4286. I am looking forward to hearing from a lot more people. I hope this helps.

That is correct. Gaussian Elimination transforms a matrix to row echelon form. Gauss-Jordan Elimination transforms matrices to their reduced row echelon form. The process is virtually identical and I think the video shows both methods. For Gaussian Elimination, just stop at the row echelon form.

@@georgefsweeney thanks for reply

You are so welcome!

I am so glad to hear it. I hope your exam went well.

Because we are breaking the interval up into 5 parts and the interval is from 0-1, we get each interval is a length of .2. So the first interval goes from 0-.2. Then we take the midpoint of each section, so that first midpoint is .1. Then, .3 and so on. You can see the explanation at about 1:15 in the video.

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You're so welcome!

Instead of having the first value for the second summation be 1, we would start with 2 and then continue until we hit whatever (the top value was). I hope I am answering your question. In the video, I start each of the second summations at 1, but you can start with any value you would like. It is the same as if we were doing a single summation.

We need to have three consecutive values that can be made using 3 and 5 cent stamps so that we can just add a 3 cent stamp in the proof to create the next value in the sequence. But we cannot create a 7 cent stamp using 3 and 5 cent stamps, so we start at 8= 5+3, 9=3*3 and 10=5*2. I hope that helps.

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I am glad it helped.

I chose 3^3 because I wanted to have e be relatively prime to 832, but at the same time I wanted it to be relatively large for the purposes of teaching the encryption and for doing calculation. You can pick any number for e that you want as long as it is relatively prime to phi.

You're very welcome!

You're welcome

You are most welcome

Thanks for the kind words, I am glad it helped.

You're welcome. My pleasure

You're welcome.

Sorry I missed these Tariq, but do you mean the cardinality? The cardinality for that set is uncountably infinite and has the same cardinality as the reals.

Rahul, I have a whole series on functions, but are there other relations other than functions or are there other topics.

Sir in our academics we have antisymmetric, reflexive ,etc and Matrix based on relations and union of relational matrices, finding dom and range of relation, equivalence relation and partial order relation,hasse diagram lattice and many more. For function chp all topics are covered on the channel. Respected sir,. it would be very helpful if you cover all the relation topics too.😊

That's great, Kendall. I am glad I could help.