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2. In each case, show that there exist constants C and k such that f(x) ≥ Cg(x) for all x > k. Note that this will show that f(x) is N(g(x)). (a) f(x) = 2x³ + 3x² + 5x + 7 and g(x) = x³ (b) f(x) = log(x² + 3x + 1) and g(x) = log x

2. In each case, show that there exist constants C and k such that f(x) ≥ Cg(x) for all x > k. Note that this will show that f(x) is N(g(x)). (a) f(x) = 2x³ + 3x² + 5x + 7 and g(x) = x³ (b) f(x) = log(x² + 3x + 1) and g(x) = log x

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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2. In each case, show that there exist constants C and k such that f(x) ≥ Cg(x) for all x > k. Note that this will show that f(x) is (g(x)). (a) f(x) = 2x³ + 3x² + 5x + 7 and g(x) = x³ (b) f(x) = log(x² + 3x + 1) and g(x) = log x
Transcribed Image Text:2. In each case, show that there exist constants C and k such that f(x) ≥ Cg(x) for all x > k. Note that this will show that f(x) is (g(x)). (a) f(x) = 2x³ + 3x² + 5x + 7 and g(x) = x³ (b) f(x) = log(x² + 3x + 1) and g(x) = log x
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