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1. Consider the curve C in the plane determined by x² + y² = (3 + 2x)² with -1 ≤ x ≤0. Give a very accurate graph of the curve indicating all intercepts and other important points. 2. Find an implicit derivative for the curve and find any critical points. 3. Find the area bounded by the curve and the y-axis.

1. Consider the curve C in the plane determined by x² + y² = (3 + 2x)² with -1 ≤ x ≤0. Give a very accurate graph of the curve indicating all intercepts and other important points. 2. Find an implicit derivative for the curve and find any critical points. 3. Find the area bounded by the curve and the y-axis.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this project, you play the role of a consultant to a manufacturer of plastics-based items. You will study a curve that forms the basis for the construction of two items the manufacturer plans to produce. In so doing, you will find implicit derivatives, find the area bounded by the axes and the curve, find the volume of a solid of revolution of the curve, and compute costs for producing the two items. 1. Consider the curve C in the plane determined by x² + y² = (3 + 2x)2 with -1 ≤ x ≤0. Give a very accurate graph of the curve indicating all intercepts and other important points. 2. Find an implicit derivative for the curve and find any critical points. 3. Find the area bounded by the curve and the y-axis. 4. Find the length of the curve C.
Transcribed Image Text:In this project, you play the role of a consultant to a manufacturer of plastics-based items. You will study a curve that forms the basis for the construction of two items the manufacturer plans to produce. In so doing, you will find implicit derivatives, find the area bounded by the axes and the curve, find the volume of a solid of revolution of the curve, and compute costs for producing the two items. 1. Consider the curve C in the plane determined by x² + y² = (3 + 2x)2 with -1 ≤ x ≤0. Give a very accurate graph of the curve indicating all intercepts and other important points. 2. Find an implicit derivative for the curve and find any critical points. 3. Find the area bounded by the curve and the y-axis. 4. Find the length of the curve C.
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