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1. Prove the following polynomial is 0(n¹). Use algebraic manipulations. P(n) = 5n -10 n³ + 20 n² + 50 n - 100 (a) Prove 0 (nª). (b) Prove (n¹).

1. Prove the following polynomial is 0(n¹). Use algebraic manipulations. P(n) = 5n -10 n³ + 20 n² + 50 n - 100 (a) Prove 0 (nª). (b) Prove (n¹).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.2: Polynomial Functinos And Their Graphs
Problem 2E: Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b)...
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Dept, NJI First 1. Prove the following polynomial is 8(*). Use algebraic manipulations. P(n)= 5n+20 ³-10 m² +10 (a) Prove O(n*). 3 2 P(x) = 5n² + 20 n°²- 10 m² +10 <5n4+201³ +10 Therefore, 5 <5n² + 201³ (1) + 10 (212) 4 3 ≤n² (5+02 +0.0000001) n4 n4 (m4 (5.2001) m2lcv (b) Prove (n*). P(n) = 5n² + 20 n²³ - 10 m² +10 3 4 4.9 m m2 10 Last Discard Neg Terms < P(x) < 5.2001 n4 m2100, (m)>) > 5n²4-10 n² Σ 5n" - 102² (+)² m2 10 (1) 2) 2 > 10 1 >n² (5-0.1) > 4.9 m² Note this Transformation may be applied only to pas Discord Pos Terms tomm. (This may be applied) to only Neg terms, m2 100
Transcribed Image Text:Dept, NJI First 1. Prove the following polynomial is 8(*). Use algebraic manipulations. P(n)= 5n+20 ³-10 m² +10 (a) Prove O(n*). 3 2 P(x) = 5n² + 20 n°²- 10 m² +10 <5n4+201³ +10 Therefore, 5 <5n² + 201³ (1) + 10 (212) 4 3 ≤n² (5+02 +0.0000001) n4 n4 (m4 (5.2001) m2lcv (b) Prove (n*). P(n) = 5n² + 20 n²³ - 10 m² +10 3 4 4.9 m m2 10 Last Discard Neg Terms < P(x) < 5.2001 n4 m2100, (m)>) > 5n²4-10 n² Σ 5n" - 102² (+)² m2 10 (1) 2) 2 > 10 1 >n² (5-0.1) > 4.9 m² Note this Transformation may be applied only to pas Discord Pos Terms tomm. (This may be applied) to only Neg terms, m2 100
1. Prove the following polynomial is 0 (n²). Use algebraic manipulations. P(n) = 5n -10 n³ + 20 n² + 50 n - 100 (a) Prove 0 (nª). (b) Prove (n¹).
Transcribed Image Text:1. Prove the following polynomial is 0 (n²). Use algebraic manipulations. P(n) = 5n -10 n³ + 20 n² + 50 n - 100 (a) Prove 0 (nª). (b) Prove (n¹).
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