Using a Tangent Line Approximation In Exercises 1-6, find the tangent line approximation T to the graph of f at the given point. Use this linear approximation to complete the table. 1.9 1.99 2 2.01 2.1 f(x) T(x) 1. f(x) = x², (2, 4) 2. f(x) x²' 2,
Using a Tangent Line Approximation In Exercises 1-6, find the tangent line approximation T to the graph of f at the given point. Use this linear approximation to complete the table. 1.9 1.99 2 2.01 2.1 f(x) T(x) 1. f(x) = x², (2, 4) 2. f(x) x²' 2,
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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![**Using a Tangent Line Approximation**
In Exercises 1–6, find the tangent line approximation \( T \) to the graph of \( f \) at the given point. Use this linear approximation to complete the table.
| \( x \) | 1.9 | 1.99 | 2 | 2.01 | 2.1 |
|--------|-----|------|---|------|-----|
| \( f(x) \) | | | | | |
| \( T(x) \) | | | | | |
**Functions and Points:**
1. \( f(x) = x^2 \), \( (2, 4) \)
2. \( f(x) = \frac{6}{x^2} \), \( \left( 2, \frac{3}{2} \right) \)
3. \( f(x) = x^5 \), \( (2, 32) \)
4. \( f(x) = \sqrt{x} \), \( \left( 2, \sqrt{2} \right) \)
5. \( f(x) = \sin x \), \( (2, \sin 2) \)
6. \( f(x) = \csc x \), \( (2, \csc 2) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd45308af-f507-4349-a094-dce43ad17ed2%2F0c098aac-097b-4499-8e74-fa84b7e5d9a5%2F5dq99q_processed.png&w=3840&q=75)
Transcribed Image Text:**Using a Tangent Line Approximation**
In Exercises 1–6, find the tangent line approximation \( T \) to the graph of \( f \) at the given point. Use this linear approximation to complete the table.
| \( x \) | 1.9 | 1.99 | 2 | 2.01 | 2.1 |
|--------|-----|------|---|------|-----|
| \( f(x) \) | | | | | |
| \( T(x) \) | | | | | |
**Functions and Points:**
1. \( f(x) = x^2 \), \( (2, 4) \)
2. \( f(x) = \frac{6}{x^2} \), \( \left( 2, \frac{3}{2} \right) \)
3. \( f(x) = x^5 \), \( (2, 32) \)
4. \( f(x) = \sqrt{x} \), \( \left( 2, \sqrt{2} \right) \)
5. \( f(x) = \sin x \), \( (2, \sin 2) \)
6. \( f(x) = \csc x \), \( (2, \csc 2) \)
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