Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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HW#13 

**Identifying Symmetries of the Curve \( r^2 = 25 \cos \theta \)** This exercise focuses on identifying the symmetrical properties of the given polar equation and sketching the corresponding curve. Below are questions designed to guide your analysis: 1. **Is the curve symmetric about the x-axis?** - No - Yes 2. **Is the curve symmetric about the y-axis?** - No - Yes 3. **Is the curve symmetric about the origin?** - Yes - No **Choose the correct graph below:** - **Graph A:** Displays a limaçon with an inner loop, symmetric about the x-axis. - **Graph B:** Illustrates a cardiod symmetric about the x-axis. - **Graph C:** Represents a four-leaved rose symmetric about both axes and the origin. - **Graph D:** Shows a lemniscate symmetric about the x-axis. Analyze and determine which graph corresponds to the given polar equation, maintaining attention to symmetry and shape characteristics.
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Transcribed Image Text:**Identifying Symmetries of the Curve \( r^2 = 25 \cos \theta \)** This exercise focuses on identifying the symmetrical properties of the given polar equation and sketching the corresponding curve. Below are questions designed to guide your analysis: 1. **Is the curve symmetric about the x-axis?** - No - Yes 2. **Is the curve symmetric about the y-axis?** - No - Yes 3. **Is the curve symmetric about the origin?** - Yes - No **Choose the correct graph below:** - **Graph A:** Displays a limaçon with an inner loop, symmetric about the x-axis. - **Graph B:** Illustrates a cardiod symmetric about the x-axis. - **Graph C:** Represents a four-leaved rose symmetric about both axes and the origin. - **Graph D:** Shows a lemniscate symmetric about the x-axis. Analyze and determine which graph corresponds to the given polar equation, maintaining attention to symmetry and shape characteristics.
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