Given the function Γ defined by Γ(x)=∫_0 ^(+∞) t^(x−1) e^(−t) dt
1. What is the domain of definition of Γ ?
2. Show that ∀x∈ DΓ, xΓ(x)=Γ(x+1) and deduce the value of Γ(n), n∈N^∗
3. Assuming ∫_0 ^(+∞) e^(−u^2 ) =((√π)/2), calculate Γ((1/2)) and deduce that
Γ(n+(1/2))=(((2n)!(√π))/(2^2^n n!))
((★BeMath⊚)/⊓)
(1) ∫ x tan^(−1) (x) dx ?
(2) Find the distance of the point
(3,3,1) from the plane Π with equation
(r^→ −i^→ −j^→ )•(i^→ −j^→ +k^→ ) = 0 , also
find the point on the plane that is
nearest to (3,3,1).