Ahhhh...that really clears things up. Thank you guys.
The function in question was f(x)=\frac{(n-1)!}{(1+x)^n}. So \sup_{-r\leq x\leq r}\frac{(n-1)!}{(1+x)^n}=\frac{(n-1)!}{(1-r)^n} The r comes from the radius of convergence of a Taylor expansion (I'm reading about where T(x) = f(x) ).
Thanks...
Let 0 < r < 1. Then \sup_{x\in[-r,r]}f(x)=f(r)}, right? However, the text I'm reading says it's f(-r). How could this be? For example, say r = 0.5, then the least upper bound of [-0.5, 0.5] is 0.5, or r, right? I don't see how it could be -r. Thanks for any help.
For an elliptic PDE Uxx + Uyy + Ux + Uy = -1 in D = {x^2 + y^2 = 1} and U = 0 on the boundary of D = {x^2 + y^2 = 1}
is it possible for me to make a change of variables and eliminate the Ux and Uy and get the Laplace equation Uaa + Ubb = 0?
I tried converting into polar coordinates, but the...
I'm confused about this question.
The problem: The sum of the rolls of a fair die exceed 300. Find the probability that at least 80 rolls were necessary.
The solution we were given is that this event is equivalent to the sum of 79 rolls being less than or equal to 300. But I don't get it...