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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Use a graphing utility to find the limit.
lim x→3+
| 6 + x |
| 3 − x |
![**Prompt:**
Use a graphing utility to find the limit.
\[ \lim_{{x \to 3^+}} \frac{6 + x}{3 - x} \]
**Explanation:**
To find the limit of the function as \( x \) approaches 3 from the right (\( 3^+ \)), you can use a graphing utility or calculator. The expression \(\frac{6 + x}{3 - x}\) is the function to be analyzed.
As \( x \) gets closer to 3 from values greater than 3, observe the behavior of the function's value. Note that the denominator \((3 - x)\) approaches zero, which often leads to an infinite limit (positive or negative infinity).
Graphing the function will show how the curve behaves near \( x = 3 \). Look for vertical asymptotes and consider the direction of the function as it approaches the value of interest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ffe93f5-5f10-4bf7-acdc-0df2fea074f3%2Ffa84cde4-0bc1-4ff3-9927-d8b75fd9576b%2Ft81awx_processed.png&w=3840&q=75)
Transcribed Image Text:**Prompt:**
Use a graphing utility to find the limit.
\[ \lim_{{x \to 3^+}} \frac{6 + x}{3 - x} \]
**Explanation:**
To find the limit of the function as \( x \) approaches 3 from the right (\( 3^+ \)), you can use a graphing utility or calculator. The expression \(\frac{6 + x}{3 - x}\) is the function to be analyzed.
As \( x \) gets closer to 3 from values greater than 3, observe the behavior of the function's value. Note that the denominator \((3 - x)\) approaches zero, which often leads to an infinite limit (positive or negative infinity).
Graphing the function will show how the curve behaves near \( x = 3 \). Look for vertical asymptotes and consider the direction of the function as it approaches the value of interest.
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