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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![**Limit Problem Explanation**
Consider the following mathematical problem:
**Problem Statement:**
If \( h(x) \to 5 \) as \( x \to 1 \) and \( k(x) \to 0^+ \) as \( x \to 1 \), then what is
\[
\lim_{{x \to 1}} \frac{{h(x)}}{{k(x)}} ?
\]
**Answer Choices:**
1. \( \frac{5}{0} \)
2. \( 0 \)
3. \( \infty \)
4. \( \frac{1}{5} \)
5. \( -\infty \)
**Solution Explanation:**
As \( x \to 1 \), the function \( h(x) \) approaches 5 and \( k(x) \) approaches 0 from the positive side. The limit in question is of the form \( \frac{5}{0^+} \). In this scenario, since the denominator approaches zero from the positive side and the numerator is a positive constant, the expression tends toward positive infinity (\( \infty \)).
Hence, the correct answer is \( \infty \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdcb89481-a91d-4bc1-bc74-4fa557807e9a%2F344dd564-058a-4d7e-89c9-49cf43222e51%2Fbib0c2k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Limit Problem Explanation**
Consider the following mathematical problem:
**Problem Statement:**
If \( h(x) \to 5 \) as \( x \to 1 \) and \( k(x) \to 0^+ \) as \( x \to 1 \), then what is
\[
\lim_{{x \to 1}} \frac{{h(x)}}{{k(x)}} ?
\]
**Answer Choices:**
1. \( \frac{5}{0} \)
2. \( 0 \)
3. \( \infty \)
4. \( \frac{1}{5} \)
5. \( -\infty \)
**Solution Explanation:**
As \( x \to 1 \), the function \( h(x) \) approaches 5 and \( k(x) \) approaches 0 from the positive side. The limit in question is of the form \( \frac{5}{0^+} \). In this scenario, since the denominator approaches zero from the positive side and the numerator is a positive constant, the expression tends toward positive infinity (\( \infty \)).
Hence, the correct answer is \( \infty \).
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