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Find the tangent to y = ((x+ 1)/ (x- 2))? at x = 3. |(Type an equation.)

Find the tangent to y = ((x+ 1)/ (x- 2))? at x = 3. |(Type an equation.)

Calculus: Early Transcendentals
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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### Problem Statement **Objective:** Find the equation of the tangent to the curve defined by the function \[ y = \left(\frac{x + 1}{(x - 2)^2}\right) \] at the point where \( x = 3 \). **Instructions:** Type your answer in the provided box. > **Note:** This problem involves finding the derivative of the function to determine the slope of the tangent line at the given point. Use principles of calculus, such as the quotient rule and power rule, to solve for the derivative before applying the tangent line formula.
Transcribed Image Text:### Problem Statement **Objective:** Find the equation of the tangent to the curve defined by the function \[ y = \left(\frac{x + 1}{(x - 2)^2}\right) \] at the point where \( x = 3 \). **Instructions:** Type your answer in the provided box. > **Note:** This problem involves finding the derivative of the function to determine the slope of the tangent line at the given point. Use principles of calculus, such as the quotient rule and power rule, to solve for the derivative before applying the tangent line formula.
Expert Solution
Step 1

Given y=((x+1)/(x-2))^(2)

We have to find tangent line as shown below 

We know that equation of line through given point and slope m is

(y-y1)=m(x-x1)

steps

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Solved in 3 steps with 2 images

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