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3. Find the least integer n such that f (x) is O(x") for each of these functions. a) f (x) = 2x³ + x² log x b) f (x) = 3x³ + (log x)* c) f (x) = (xª + x² + 1)/(x³ + 1) d) f (x) = (x* + 5 log x)/(x + 1)

3. Find the least integer n such that f (x) is O(x") for each of these functions. a) f (x) = 2x³ + x² log x b) f (x) = 3x³ + (log x)* c) f (x) = (xª + x² + 1)/(x³ + 1) d) f (x) = (x* + 5 log x)/(x + 1)

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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Pls, help me answer two questions about Discrete Mathematics !!!

3. Find the least integer n such that f (x) is O(x") for each of these functions. a) f (x) = 2x³ + x² log x b) f (x) = 3x³ + (log x)* c) f (x) = (x* + x² + 1)/(x³ + 1) d) f (x) = (x* + 5 log x)/(x* + 1)
Transcribed Image Text:3. Find the least integer n such that f (x) is O(x") for each of these functions. a) f (x) = 2x³ + x² log x b) f (x) = 3x³ + (log x)* c) f (x) = (x* + x² + 1)/(x³ + 1) d) f (x) = (x* + 5 log x)/(x* + 1)
6. Give as good a big-O estimate as possible for each of these functions. a) (n² + 8)(n + 1) b) (n log n + n²)(n³ + 2) c) (n! + 2")(n³ + log(n² + 1))
Transcribed Image Text:6. Give as good a big-O estimate as possible for each of these functions. a) (n² + 8)(n + 1) b) (n log n + n²)(n³ + 2) c) (n! + 2")(n³ + log(n² + 1))
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