(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
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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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