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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faad9e4ed-ed50-4fe3-96ca-72ed3d364f6f%2F701e4ca6-6a41-448c-9106-f5291e2388de%2Fugng2ul_processed.png&w=3840&q=75)
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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