1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10
1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10
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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1. Prove the following polynomial is e(n). Use algebraic manipulations.
P(n)=5n+20 n³ - 10 n² + 10
(a) Prove 0(n*).
(b) Prove (n*).
Therefore,
4
3
P(n) = 5n²+ 20n - 10 m² +10
2
<5n4
+201³
+10
2
4
3
P(n) = 5n²+ 20 m²
3
<5n4 +201³ (^_) + 10 (212) 4
101)
< n²4 (5+02 + 0.000000,
<m² (52001)
>n4 (5-0.1)
4
> 4.9 n
of 6
4.9 n
M2lcv
1
OD
2
> 5n²4-10 n²
2
2 n
Σ 5n²-101² (70)² 7210, (+)2)
>
10
10 m² +10
m310
< P(n) < 5.2001 n'
Discard Neg Terms
m2100, (n))
Note this
transformatio
may be applied
only to pas
Discord Pos Terus
This
man
be applied)
to only Nag terms,
m> 100
Expert Solution

Step 1: Step 1
To show that:
We will use the definition of big oh notation to show this, we will find a positive constant (say C) and a real number N such that
To show:
In the above step,
Assume n≥100 then
So for n≥100 ,
Hence, for
Thus, P(n) = O(n^4)
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