2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if and only if n and k are relatively prime.
Let f and g be differentiable on R such that f(1) = g(1), and f'(x) < '() for all r ER. Prove that f(x) = g(2) for 3 >1.
Let this cluster to be a subspace of V. Find an orthonormal base for W. V = R3 ve W =< (1,0, -1),(0,1, -1) >
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Problem 5. Let a < b and c > 0 and let f be integrable on [ca, cb]. Show that f c Ca where g(a) f(ex)
an (4) Let F be ordered field. Prove that the statement Vo: ZX\x6F*XWye FtX &<y)->(<y') is true (hist: Factor Y-X out of yº-x")
Help please! Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
Prove by induction that 1 1 15 15 + 1 35 35 + ... + = n 2n + 1 for every n > 1 4n2
If a and b are real numbers and 1 < a <b, then a-1 > b-1. Proof by contradiction.
Use induction to prove that for m > 5, 5m > 25m?.