(1)
Let a, b anc c be the lengths of the sides of a triangle with inradius r.
Prove a^6 + b^6 + c^6 ≧ 5184*r^6.

(2)
Suppose that f : [0,1] → R is a differentiable function with continuous derivative and with
　　　∫[0,1] f(x)dx = ∫[0,1] xf(x)dx = 1.
Prove that
　　　∫[0,1] |f'(x)|^3 dx ≧ {128/(3π)}^2.

(3)
Calclate lim[x→∞] (Σ[n=1 to ∞] (x/n)^n )^(1/x).

(4)
Evaluate ∫[0, π/2] (sin x)/(1 + sqrt{sin 2x}) dx.

(5)
Calclate ∫[0,∞]∫[0,∞] (sin x * sin y * sin(x+y))/{xy(x+y)} dx dy.

(6)
Calclate Σ[n=1 to ∞] {2^(2n-1)/(2n+1)}*{(n-1)!/(2n-1)!!}^2 = π-2.

( ﾟ∀ﾟ) ｳﾋｮｯ！