For each function f, give O(f) using any of the properties in the last 4 slides. In each case, identify the properties used. a) f(x) = (3x3+2)7 b) f(x) = 22^x+ 2x c) f(x) = (x+xlog2x)2
For each function f, give O(f) using any of the properties in the last 4 slides. In each case, identify the properties used. a) f(x) = (3x3+2)7 b) f(x) = 22^x+ 2x c) f(x) = (x+xlog2x)2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For each function f, give O(f) using any of the properties in the last 4 slides. In
each case, identify the properties used.
a) f(x) = (3x3+2)7
b) f(x) = 22^x+ 2x
c) f(x) = (x+xlog2x)2
Expert Solution
Step 1
We know, f(x) = O(g(x)) if f(x) < cg(x) for some positive integer c, and x > x0 for some x0.
(a) f(x) = (3x3 + 2)7 < (3x3 + x3)7 for x > 21/3
= 47x21 = 16384x21
Hence, by definition, f(x) = O(x21)
[Here, c = 16384, x0 = 21/3]
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