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a.) What it the probability that heads will occur exactly three of the four times?
b.) What are the odds for heads occuring exactly three times?
c.) What are the odds against heads occuring exactly three times?
I think i have the right answers, but i would like to see what someone else gets.....Someone answer ASAP!
First, let's consider the function f:R → R given by f(x) = x² sin(1/x) if x ≠ 0 and f(0) = 0. Then, for x ≠ 0, f'(x) 2x sin(1/x) - x² cos(1/x) (1/x²) = 2x sin(1/x) - cos(1/x). So, f' doesn't have a limit at x = 0. But since the sine function is bounded, then lim (x → 0) (f(x) - f(0))/(x - 0) = lim (x → 0) x sin(1/x) = 0, so that f'(0) = 0. Therefore, f is differentiable everywhere on R, though f' is discontinuous at x = 0
Now, if we extend the domain of f to the complexes, f(z) = z² sin(1/z) if z ≠ 0, f(0) = 0, we we still have f'(z) = 2z sin(1/z) - cos(1/z) for z ≠ 0 and f'(0) = 0. Since f' is discontinuous on the real line, it's discontinuous on C. But we have f differentiable everywhere on C, so that it's complex analytic. We know complex analytic functions are infinitely differentiable an so their derivatives, including f', are continuous everywhere on C. Therefore, we have an apparent contradiction. What's the flaw in my reasoning? I can't see anything wrong.
Hello,
I am designing a website and I have decided to use Helvetica Neue. Will this font show up on Windows?
What I am basically asking is that is Helvetica Neue with all the bundled styles such as 'Regular', 'Light', 'UltraLight', 'Italic', 'Light Italic', 'UltraLight Italic' etc. a Windows font?
Thanks!
Hello,do u knw any website that allows music that is safe to use in youtube videos? I knw one such website , which is called jamendo.com.Unfortunatly there arent the artiste or songs there that im lookin for, so can u suggest me some websites plz??
Thnx alot !
I personally think the author lacks imagination and is demented. (yes i know i will get severely yelled at by all the crazed, brainwashed, demented fans...) The books are not very good, and their plots are somewhat...erm... stupid. So, someone who is obsessed, please tell me why. Or someone not obsessed, try to imagine, or you can always agree with me.