Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones.
a) x/log x → 0 as x → 0.
b) If n ∈ N, then sin(1/x)/xn → 0 as A: → ∞.
c) xlogx → 0 as x → 0+.
d) If there is a β > 0 such that f'(x) > β for all x ∈ (0, ∞), then x2/f(x) → ∞ as x → ∞.