Find the limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) < + 2x² lim X→8 6x1
Find the limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) < + 2x² lim X→8 6x1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Calculating the Limit of a Function as x Approaches Infinity**
Consider the following limit as \( x \) approaches infinity:
\[ \lim_{{x \to \infty}} \frac{\sqrt{x + 2x^2}}{6x - 1} \]
### Instructions:
- If the limit is infinite, enter \(\infty\) or \(-\infty\), as appropriate.
- If the limit does not exist otherwise, enter DNE.
### Steps to Solve:
1. Simplify the expression inside the square root and the denominator by factoring out \(x^2\) from the terms within the square root.
2. Evaluate the limit by dividing the numerator and the denominator by \( x \).
3. Solve for the value as \( x \) approaches infinity.
Understanding this process is crucial for mastering limits in differential calculus and functions approaching infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00067d91-5c79-4b53-8e03-40299a52da99%2F64910081-77f4-4c71-8252-148b52042110%2F4vuvlym_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating the Limit of a Function as x Approaches Infinity**
Consider the following limit as \( x \) approaches infinity:
\[ \lim_{{x \to \infty}} \frac{\sqrt{x + 2x^2}}{6x - 1} \]
### Instructions:
- If the limit is infinite, enter \(\infty\) or \(-\infty\), as appropriate.
- If the limit does not exist otherwise, enter DNE.
### Steps to Solve:
1. Simplify the expression inside the square root and the denominator by factoring out \(x^2\) from the terms within the square root.
2. Evaluate the limit by dividing the numerator and the denominator by \( x \).
3. Solve for the value as \( x \) approaches infinity.
Understanding this process is crucial for mastering limits in differential calculus and functions approaching infinity.
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