I tried to integrate that function, but i could not. I putted into Wolfram Mathematica and the result was longer than expected. Clearly this integral isn't very easy to resolve, true?
What happens when the inequality is false , say the the integral you start with ( the know) is covergent and you work that until you see that the inequality does not hold true , would that mean the improper integral is divergent ?
How do they get linearly independent on (-Infiniti, Infiniti) ? Please upload some videos if you can. If you can't, it's ok. I did research on UA-cam, I couldn't find one good video. Thank you so much tho. Take care. I've been watching your videos since spring 2016. You are the best.
blackpenredpen thank you. I'm working on homogeneous second order linearly dependent and linearly independent. I knew all the basic stuff, but some books wrote really hard theorem. I don't understand. It's about f(t)=t^2 if t=0 and g(t)= 2 t^2, if t= 0 are linearly independent on (-Infiniti, +infiniti). I only understand they are linearly dependent on (-infinit, 0) and (0, + Infiniti).
vivelly wang vivelly wang hi vivelly. It's really late now and I prob won't be able to be in school this weekend to make more videos. But the way to do that is, since t^3 and 4t^4 are linearly independent, thus those two piecewise functions are overall linearly independent.
Perhaps you have a theorem like this in the book, which says if W(f,g) is not zero at some x_0 on the interval I, then f and g are linearly independent on I
I need more teachers like you. You explain things a lot better than a large majority of the teachers that I have had in the past
I've watched a few videos on the comparison test and yours are by far the most helpful ! thank you 😊
Thanks, amazing teaching!
check out example 3 ua-cam.com/video/5GP963kPsPE/v-deo.html
good thing blackpenredpen and youtube exist
I tried to integrate that function, but i could not. I putted into Wolfram Mathematica and the result was longer than expected. Clearly this integral isn't very easy to resolve, true?
Juan José Miguel well thats called divergent :)
ua-cam.com/video/5GP963kPsPE/v-deo.html
What happens when the inequality is false , say the the integral you start with ( the know) is covergent and you work that until you see that the inequality does not hold true , would that mean the improper integral is divergent ?
i love your videos! (side note: slight error at 6:10 ? shouldn't it be x^5 ≥ x^5 - 1 ? same conclusion though in the end)
DestinyQx yea. I didn't square both sides tho. I just rewrote the 5/2 power with sqrt lol
thanks for videos! i began studying diff eq because of your vids.. maybe one day i'll study linear algebra too
Thank you thank you thank you omg thank you SO much
hey btw you have really helped me alot.thank u
ok，take your time Thanks. Take care
And he's sooo funnny :-)))))!!!
what would you do if the equality check gives you false?
How do they get linearly independent on (-Infiniti, Infiniti) ? Please upload some videos if you can. If you can't, it's ok. I did research on UA-cam, I couldn't find one good video. Thank you so much tho. Take care. I've been watching your videos since spring 2016. You are the best.
Can you do some differential equations?
vivelly wang I am uploading, some second order and reduction of orders. What topics did u have in mind?
blackpenredpen thank you. I'm working on homogeneous second order linearly dependent and linearly independent. I knew all the basic stuff, but some books wrote really hard theorem. I don't understand. It's about f(t)=t^2 if t=0 and g(t)= 2 t^2, if t= 0 are linearly independent on (-Infiniti, +infiniti). I only understand they are linearly dependent on (-infinit, 0) and (0, + Infiniti).
vivelly wang vivelly wang hi vivelly. It's really late now and I prob won't be able to be in school this weekend to make more videos. But the way to do that is, since t^3 and 4t^4 are linearly independent, thus those two piecewise functions are overall linearly independent.
Perhaps you have a theorem like this in the book, which says if W(f,g) is not zero at some x_0 on the interval I, then f and g are linearly independent on I
Thus u can show that W(x^3,4x^4) is not zero on (0 to inf) thus f and g are L.I.
Wola mzukulu ka Chan
i thought it would be 2 instead of 1at 3.15 Since a =2
It has no elementary solution.
我覺得右邊的寫法有點讓誤解：第一條式子並不需要大於等於零，零只是一般來說方便驗證，只要是有限大的數就可以。第二條式子小於零也可以類似地用，只是不等式方向要相反。與第一式相同地，這也不必需是零。
mu test will be much easier
Well, you can leave out some details which are obvious in the process