1a) If 0<p<q, then Integral [upper limit: p, lower limit: 0] f(x)dx < integral [upper limit: q, lower limit: 0] f(x)dx.
b) If 0<p<q, then log p< log q.
c) If n^3 - n is divisible by 4, then n must be divisible by 4.
d) If n is a positive integer, then n^3 - n is divisible by 3.
2. Given that f(x) = x/(x + 1), find f^2(x) i.e. f(f(x)). Find also f^3(x) and suggest a possible form for f^n(x). Prove that your result is correct by M.I.
更新1:
∫[0,q] f(x) dx = ∫[0,p] f(x) dx + ∫[p,q] f(x) dx Why do we need to add ∫[p,q] f(x) dx? Also, why do ∫[0,p] f(x) dx , the upper limit is 0 and the lower limit is p/q? Could u explain 1b)' again?
更新2:
Sorry! Sould be Could u explain 1a)' again? not 1b)
