Given the function
f(x) = ((ln x)/(x−1))
(a) State the domain D_f of f.
(b) Find lim_(x→∞) ((ln x)/(x−1)). State its asymptotes.
(c) Draw up a variation table for the curve y = f(x).
Working individually, A, B and C can
finish a piece of work in 16 days, 20 days
and 30 days respectively. In how many
days can A, B and C together complete
a work which is 3(1/2) times the previous
work?
Given the sequence (U_n )_(n∈N) defined by U_0 =1 and
U_(n+1) =f(U_n ) where f(x)=(x/((x+1)^2 ))
Show by mathematical induction that ∀n∈N^∗
0<U_n ≤(1/n)