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(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

(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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Let ƒ : (1, +∞) → R be a (i) Assume that f'(x)| ≤ (ii) Assume that |f'(x)| ≤ Justify your answer. differentiable function. 1 x² for all x > 1. Show that lim (ƒ(x³) — ƒ(x³)) = 0. 1 for all x > 1. Is it necessarily true that x lim (f(x5)-f(x³)) = 0? x → +∞ 8+←
Transcribed Image Text:(a) Let ƒ : (1, +∞) → R be a (i) Assume that f'(x)| ≤ (ii) Assume that |f'(x)| ≤ Justify your answer. differentiable function. 1 x² for all x > 1. Show that lim (ƒ(x³) — ƒ(x³)) = 0. 1 for all x > 1. Is it necessarily true that x lim (f(x5)-f(x³)) = 0? x → +∞ 8+←
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