Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Please show all work and steps clearly. The format and steps have not always been clear. Thank you.

**Problem Statement:**

Find the equation of the tangent line to the curve (a lemniscate) 

\[ 2(x^2 + y^2)^2 = 25(x^2 - y^2) \]

at the point \((3, -1)\).

**Solution Format:**

The equation of this tangent line can be written in the form \( y = mx + b \)

**Where:**

\( m \) is: [Blank space for students to fill]

\( b \) is: [Blank space for students to fill]

**Instructions:**

- Calculate the derivative of the given lemniscate equation to find the slope \( m \) at the point \((3, -1)\).
- Use the point-slope form to determine the y-intercept \( b \) once the slope \( m \) is known.
- Provide your final answer in the format \( y = mx + b \) filling in the blanks provided.
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Transcribed Image Text:**Problem Statement:** Find the equation of the tangent line to the curve (a lemniscate) \[ 2(x^2 + y^2)^2 = 25(x^2 - y^2) \] at the point \((3, -1)\). **Solution Format:** The equation of this tangent line can be written in the form \( y = mx + b \) **Where:** \( m \) is: [Blank space for students to fill] \( b \) is: [Blank space for students to fill] **Instructions:** - Calculate the derivative of the given lemniscate equation to find the slope \( m \) at the point \((3, -1)\). - Use the point-slope form to determine the y-intercept \( b \) once the slope \( m \) is known. - Provide your final answer in the format \( y = mx + b \) filling in the blanks provided.
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