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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Q7. Please answer all the parts to this question
![**Problem Statement:**
Find the points on the lemniscate where the tangent is horizontal. (Order your answers from smallest to largest \( x \), then from smallest to largest \( y \).)
\[ 8(x^2 + y^2)^2 = 25(x^2 - y^2) \]
**Graph:**
- The graph is a lemniscate centered at the origin.
- The lemniscate resembles the shape of a figure-eight or an infinity symbol.
- The axes are marked, with \( x \)-axis ranging from \(-2\) to \(2\) and \( y \)-axis ranging from \(-0.6\) to \(0.6\).
- Tangent lines to this curve at the points of interest will be horizontal.
**Solution Boxes:**
The points should be listed as coordinates \((x, y)\) in the following format:
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87311036-785b-48b7-ad0a-ffb7f8402d00%2F4e852316-35e3-4d47-b3cb-26e84187e47d%2Fcbu4kgd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the points on the lemniscate where the tangent is horizontal. (Order your answers from smallest to largest \( x \), then from smallest to largest \( y \).)
\[ 8(x^2 + y^2)^2 = 25(x^2 - y^2) \]
**Graph:**
- The graph is a lemniscate centered at the origin.
- The lemniscate resembles the shape of a figure-eight or an infinity symbol.
- The axes are marked, with \( x \)-axis ranging from \(-2\) to \(2\) and \( y \)-axis ranging from \(-0.6\) to \(0.6\).
- Tangent lines to this curve at the points of interest will be horizontal.
**Solution Boxes:**
The points should be listed as coordinates \((x, y)\) in the following format:
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]
- \((x, y) = \) [ ]
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