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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2.3 Q5) Hey, I need help with the following calc problem. Thank you!
![# Finding the Equation of a Tangent Line to a Curve
## Problem Statement
Find an equation of the tangent line to the curve at the given point.
\[ y = \frac{(x - 1)}{(x - 2)} \quad \text{at} \quad (3, 2) \]
Below the text, a blank rectangle is shown, indicating where additional explanations, calculations, or graphical representations can be added.
---
### Solution Steps
1. **Identify the given function and point:**
- Function: \( y = \frac{(x - 1)}{(x - 2)} \)
- Point: \( (3, 2) \)
2. **Find the derivative \( y' \) of the function to get the slope of the tangent line at the given point.**
3. **Evaluate the derivative at \( x = 3 \) to find the slope of the tangent line.**
4. **Use the point-slope form of the equation of a line:**
- Point-slope form: \( y - y_1 = m(x - x_1) \)
- Where \( (x_1, y_1) \) is the given point and \( m \) is the slope.
5. **Substitute the values into the point-slope form to find the equation of the tangent line.**
---
This page provides a step-by-step approach to solve for the equation of the tangent line to the given curve at a specific point, including the necessary differentiation and substitution steps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad7698e6-8405-4b47-832b-91e13474f515%2F9460cec5-eabc-4f48-a2e5-dcec0e23a43f%2Fuu8ns4n_processed.png&w=3840&q=75)
Transcribed Image Text:# Finding the Equation of a Tangent Line to a Curve
## Problem Statement
Find an equation of the tangent line to the curve at the given point.
\[ y = \frac{(x - 1)}{(x - 2)} \quad \text{at} \quad (3, 2) \]
Below the text, a blank rectangle is shown, indicating where additional explanations, calculations, or graphical representations can be added.
---
### Solution Steps
1. **Identify the given function and point:**
- Function: \( y = \frac{(x - 1)}{(x - 2)} \)
- Point: \( (3, 2) \)
2. **Find the derivative \( y' \) of the function to get the slope of the tangent line at the given point.**
3. **Evaluate the derivative at \( x = 3 \) to find the slope of the tangent line.**
4. **Use the point-slope form of the equation of a line:**
- Point-slope form: \( y - y_1 = m(x - x_1) \)
- Where \( (x_1, y_1) \) is the given point and \( m \) is the slope.
5. **Substitute the values into the point-slope form to find the equation of the tangent line.**
---
This page provides a step-by-step approach to solve for the equation of the tangent line to the given curve at a specific point, including the necessary differentiation and substitution steps.
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