murshid

I am looking for cases (if any) where patients were pronounced dead by doctors and then came back to life. Are there any such cases? I am not looking for cases of near-death experiences.

I loved David Acheson's "The Wonder Book of Geometry". Can you recommend other books like that?

Have you tried Khan Academy?

Can anyone suggest a good lecture series on Complex Analysis on YouTube? I have already searched on YouTube myself, and there are a few. But I wanted to know if any of you would recommend some particular lecture series which you consider to be good.

That's the part I did not understand. I did draw a diagram, but got confused by the language. So, I attached the diagram. O is the point where the lifeguard is. A is the point where the shark is at t = 0. So, OA = 90 feet. B is the point where the shark is 150 feet away from the lifeguard. So, OB = 150 feet. AB = sqrt (OB2 - OA2) = sqrt (1502 - 902) = 120 feet Since the shark is moving at a constant speed of 30 ft./s, it would reach B at t = 4 ; [ t = d/v =120/30 = 4 ] So, in 4 seconds, the shark went 150-90 = 60 feet further away from the lifeguard. The speed at which the shark is moving away from the lifeguard at B = 60/4 = 15 ft./s Is that it?

Here is the problem: Now, if the speed is constant, then shouldn't the answer be 30 feet per second no matter where the shark is?

[math]\frac{\pi^{2}}{6}[/math] (test)

\frac{\pi^{2}}{6} (test) What am I doing wrong? Why isn't it working? .

That sounds a bit weird.

I just wanted to learn some hyperbolic geometry by myself. And I found this YouTube channel which has many lectures on many different math topics: https://www.youtube.com/user/njwildberger Has anyone tried his lectures before? Is he any good?

1. How common is schizophrenia among children (e.g. 10-15 year old or even younger)? 2. Does schizophrenia has any cure? Is there any instance of a person being fully cured of it? Thanks in advance!

I was also not sure what the article (http://news.discovery.com/space/do-we-live-in-a-spinning-universe-110708.html) meant by "the universe". Perhaps they meant the observable universe, although I can't be sure. .

. What do you guys think of this news: "Is the Universe Spinning?" What is the universe spinning with respect to? Has there been any further developments regarding the discovery? .

Thanks a lot for your help, but I have come here to tell you guys that I've just figured out my mistake. I got the areas of the rectangles wrong. The sum of the areas would be, [math]A_r = (a - ar)a^n + (ar - ar^2)(ar)^n + (ar^2 - ar^3)(ar^2)^n + \cdots[/math] [math]A_r = a^{n+1}(1 - r) \left(1 + r^{n+1} + r^{2(n+1)} + \cdots \right)[/math] [math]A_r = \frac{a^{n+1}(1 - r)}{1 - r^{n+1}}[/math] DrRocket, yes, it is a crude approximation, which is why Fermat reasoned that the width of each rectangle must be made small. And for this, r must be close to 1. [math]A_r = \frac{a^{n+1}(1 - r)}{1 - r^{n+1}}[/math] [math]A_r = \frac{a^{n+1}(1 - r)}{(1 - r)(1 + r + r^2 + \cdots + r^n)}[/math] [math]A_r = \frac{a^{n+1}}{1 + r + r^2 + \cdots + r^n}[/math] As we let [imath]r \rightarrow 1[/imath], each term is the denominator tends to 1, resulting in, [math]A = \frac{a^{n+1}}{n + 1}[/math] And that is the integration formula [math]\int_{0}^{a} x^n dx = \frac{a^{n+1}}{n + 1}[/math] .

You added a finite geometric series. I added an infinite one. .