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 1: Find the Equation of the Tangent Line
**Problem Statement:**
Find the equation of the tangent line to the curve
\[ y = \sqrt{\sin^2{x} + x^2} \]
at the point
\[ (\pi, \pi) \].
---
**Explanation:**
1. **Given Function:**
The function is given by:
\[
y = \sqrt{\sin^2{x} + x^2}
\]
2. **Point of Tangency:**
The point at which we need to find the tangent line is:
\[
(\pi, \pi)
\]
3. **Approach:**
To find the tangent line equation at a specific point, we need to:
- Calculate the derivative of the function to find the slope at the given point.
- Use the point-slope form of the line equation to determine the equation of the tangent line.
Note:
- The derivative of the function \( y \) will be needed to find the slope \( m \).
- The point-slope form of a line is \( y - y_1 = m(x - x_1) \).
**Graphs and Diagrams:**
There are no visual graphs or diagrams provided in this problem statement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e9d947d-304f-415e-95bf-140f5d3b17e4%2Fe32ae63e-662c-4da8-a2d5-6e5c7fb000ae%2For7429i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 1: Find the Equation of the Tangent Line
**Problem Statement:**
Find the equation of the tangent line to the curve
\[ y = \sqrt{\sin^2{x} + x^2} \]
at the point
\[ (\pi, \pi) \].
---
**Explanation:**
1. **Given Function:**
The function is given by:
\[
y = \sqrt{\sin^2{x} + x^2}
\]
2. **Point of Tangency:**
The point at which we need to find the tangent line is:
\[
(\pi, \pi)
\]
3. **Approach:**
To find the tangent line equation at a specific point, we need to:
- Calculate the derivative of the function to find the slope at the given point.
- Use the point-slope form of the line equation to determine the equation of the tangent line.
Note:
- The derivative of the function \( y \) will be needed to find the slope \( m \).
- The point-slope form of a line is \( y - y_1 = m(x - x_1) \).
**Graphs and Diagrams:**
There are no visual graphs or diagrams provided in this problem statement.
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