(a) Let f: (1, +∞) → R be a differentiable function. 1 (i) Assume that |ƒ'(x)| ≤ for all x > 1. Show that x² (ii) Assume that |f'(x)| ≤ Justify your answer. lim (f(x³) — ƒ(x³)) = 0. for all > 1. Is it necessarily true tha lim_ (ƒ(x³) — ƒ(x³)) = 0? x→+∞ 8+←8

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