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1. 2. n−1 4 nh+n-6 7n+1 n² +1

1. 2. n−1 4 nh+n-6 7n+1 n² +1

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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Determine whether the given limits exist and find their values. Give a clear explanation.

 

The image contains mathematical expressions that appear to be part of a problem set. Below are the transcriptions of the expressions: 1. \(\frac{n^4 - 1}{n^4 + n - 6}\) This expression is a fraction with a polynomial in both the numerator and the denominator. The numerator is \(n^4 - 1\), and the denominator is \(n^4 + n - 6\). 2. \(\frac{7n + 1}{\sqrt{n^2 + 1}}\) This expression is also a fraction. The numerator is a linear expression, \(7n + 1\), and the denominator is the square root of a quadratic expression, \(\sqrt{n^2 + 1}\).
Transcribed Image Text:The image contains mathematical expressions that appear to be part of a problem set. Below are the transcriptions of the expressions: 1. \(\frac{n^4 - 1}{n^4 + n - 6}\) This expression is a fraction with a polynomial in both the numerator and the denominator. The numerator is \(n^4 - 1\), and the denominator is \(n^4 + n - 6\). 2. \(\frac{7n + 1}{\sqrt{n^2 + 1}}\) This expression is also a fraction. The numerator is a linear expression, \(7n + 1\), and the denominator is the square root of a quadratic expression, \(\sqrt{n^2 + 1}\).
Expert Solution
Step 1: Basic bounding

We shall divide and using the highest power of n and then find the limit

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