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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![**Transcription of Math Problems**
**Problem 14:**
"The figure above shows the graph of the polynomial function \( f \). For which value of \( k \) is it true that \( f(k) < f(x) \) for all \( x \neq k \)?"
Options:
- (A) \( a \)
- (B) \( b \) [Correct answer circled]
- (C) \( c \)
- (D) \( d \)
- (E) \( e \)
**Problem 15:**
"What is the slope of the line tangent to the curve \( x^2 + 2xy = 2 - 2 \sin y \) at the point \((2,0)\)?"
Options:
- (A) \(-2\)
- (B) \(0\) [Correct answer circled]
- (C) \(\frac{1}{2}\)
- (D) \(\frac{1}{3}\)
- (E) \(2\)
Solution shown:
\( y = x - 2 \cos y \cdot y' \)
Steps:
- At the point \( (2,0) \):
1. Substitute \( x = 2 \) and \( y = 0 \).
2. \( y = 2 - 2 \cos y \cdot y' \)
3. When \( y = 0 \), \( \cos y = 1 \).
4. \( y' = 0 \)
**Problem 16:**
"The line \( y = 5 \) is a horizontal asymptote to the graph of which of the following functions?"
Options:
- (A) \( y = \sin(5x) \)
- (B) \( y = 5x \)
- (C) \( y = \frac{5}{x} \) [Correct answer circled]
- (D) \( y = \frac{5x}{x - 5} \)
No additional solution details or graphs were included for Problem 16.
---
This interpretation maintains the key components and selections of the original document for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc847fc0-878e-4f0b-8ce5-aa2a2b5a45b9%2Fe1b56bcb-cea3-4a99-9ac2-63ef3bfc44a2%2Fzsemixs.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription of Math Problems**
**Problem 14:**
"The figure above shows the graph of the polynomial function \( f \). For which value of \( k \) is it true that \( f(k) < f(x) \) for all \( x \neq k \)?"
Options:
- (A) \( a \)
- (B) \( b \) [Correct answer circled]
- (C) \( c \)
- (D) \( d \)
- (E) \( e \)
**Problem 15:**
"What is the slope of the line tangent to the curve \( x^2 + 2xy = 2 - 2 \sin y \) at the point \((2,0)\)?"
Options:
- (A) \(-2\)
- (B) \(0\) [Correct answer circled]
- (C) \(\frac{1}{2}\)
- (D) \(\frac{1}{3}\)
- (E) \(2\)
Solution shown:
\( y = x - 2 \cos y \cdot y' \)
Steps:
- At the point \( (2,0) \):
1. Substitute \( x = 2 \) and \( y = 0 \).
2. \( y = 2 - 2 \cos y \cdot y' \)
3. When \( y = 0 \), \( \cos y = 1 \).
4. \( y' = 0 \)
**Problem 16:**
"The line \( y = 5 \) is a horizontal asymptote to the graph of which of the following functions?"
Options:
- (A) \( y = \sin(5x) \)
- (B) \( y = 5x \)
- (C) \( y = \frac{5}{x} \) [Correct answer circled]
- (D) \( y = \frac{5x}{x - 5} \)
No additional solution details or graphs were included for Problem 16.
---
This interpretation maintains the key components and selections of the original document for educational purposes.
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