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Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O None of these.

Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O None of these.

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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**Problem Statement:** Indicate the smallest integer \( n \) such that \[ f(x) = \left(\frac{6x^2 + 4x}{x^4 - 4x}\right)^3 \in O(x^n). \] **Multiple Choice Options:** - ○ \( n = 4 \) - ○ \( n = 2 \) - ○ \( n = 1 \) - ○ \( n = 6 \) - ○ None of these.
Transcribed Image Text:**Problem Statement:** Indicate the smallest integer \( n \) such that \[ f(x) = \left(\frac{6x^2 + 4x}{x^4 - 4x}\right)^3 \in O(x^n). \] **Multiple Choice Options:** - ○ \( n = 4 \) - ○ \( n = 2 \) - ○ \( n = 1 \) - ○ \( n = 6 \) - ○ None of these.
Expert Solution
Step 1

f(x) = (6x2 + 4x)3/(x4 - 4x) 

       = {2x(3x + 2)}3/{x(x3 - 4)}

       = 8x3(3x + 2)3/{x(x3 - 4)}

       = 8x2(3x + 2)3/(x3 - 4) 

 

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