For question 1 to question 2, determine f(x) is 0(g(x)), find witnesses C and k such that If(x)l < C[g(x)l, whenever x > k. 1. Determine whether each of these functions has a big-O relationship. (a) f(x) = 5,g(x) = x (b) f(x) = 2x – 7,g(x) = x (c) f(x) = x² + x+ 2, g(x) = x (d) f(x) = 3x log(x),g(x) = x²
For question 1 to question 2, determine f(x) is 0(g(x)), find witnesses C and k such that If(x)l < C[g(x)l, whenever x > k. 1. Determine whether each of these functions has a big-O relationship. (a) f(x) = 5,g(x) = x (b) f(x) = 2x – 7,g(x) = x (c) f(x) = x² + x+ 2, g(x) = x (d) f(x) = 3x log(x),g(x) = x²
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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![For question 1 to question 2, determine f(x) is 0(g(x)), find witnesses C and k such that
If(x)l < C[g(x)l, whenever x > k.
1. Determine whether each of these functions has a big-O relationship.
(a) f(x) = 5, g(x) = x
(b) f(x) = 2x – 7, g(x) = x
(c) f(x) = x² + x + 2, g(x) = x
(d) f(x) = 3x log(x),g(x) = x²
2. Find the least integer n such that f (x) is 0(x") for each of these functions.
(a) f(x) = 3x²log (x) + 2x³
(b) f(x) =
x3-1
[Hint: Simplify this function first.]
x-1
For question 3 to question 4, determine f(x) is N(g(x)), find witnesses Cand k such that
If(x)| > C[g(x)l, whenever x > k.
3. Determine whether each of these functions has a big-2 relationship.
(a) f(x) = 5, g(x) = x
(b) f(x) = 2x – 7, g(x) = x
(c) f(x) = x² + x + 2, g(x) = x
(d) f(x) = 3x log(x),g(x) = x
4. Find the largest integer n such that f (x) is N(x") for each of these functions.
(a) f(x) = 3x²log (x) + 2x³
(b) f(x) = 3x² + 2x + 2
6. f(x) = (x + x²)(logx + x), determine function g(x) that is f (x) is O(g(x)), find witnesses
Cz and C2 and k such that C,|g(x)| < If(x)| < Cz[g(x)l, whenever x > k. [Hint: Simplify
function f(x) first.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0fa7382-d02f-443d-9e9f-3c8c91e7a245%2Fa45ccfb8-191e-4c01-af17-2f6ed6f137c0%2Fnd75a5k_processed.png&w=3840&q=75)
Transcribed Image Text:For question 1 to question 2, determine f(x) is 0(g(x)), find witnesses C and k such that
If(x)l < C[g(x)l, whenever x > k.
1. Determine whether each of these functions has a big-O relationship.
(a) f(x) = 5, g(x) = x
(b) f(x) = 2x – 7, g(x) = x
(c) f(x) = x² + x + 2, g(x) = x
(d) f(x) = 3x log(x),g(x) = x²
2. Find the least integer n such that f (x) is 0(x") for each of these functions.
(a) f(x) = 3x²log (x) + 2x³
(b) f(x) =
x3-1
[Hint: Simplify this function first.]
x-1
For question 3 to question 4, determine f(x) is N(g(x)), find witnesses Cand k such that
If(x)| > C[g(x)l, whenever x > k.
3. Determine whether each of these functions has a big-2 relationship.
(a) f(x) = 5, g(x) = x
(b) f(x) = 2x – 7, g(x) = x
(c) f(x) = x² + x + 2, g(x) = x
(d) f(x) = 3x log(x),g(x) = x
4. Find the largest integer n such that f (x) is N(x") for each of these functions.
(a) f(x) = 3x²log (x) + 2x³
(b) f(x) = 3x² + 2x + 2
6. f(x) = (x + x²)(logx + x), determine function g(x) that is f (x) is O(g(x)), find witnesses
Cz and C2 and k such that C,|g(x)| < If(x)| < Cz[g(x)l, whenever x > k. [Hint: Simplify
function f(x) first.]
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