Use linear approximation, i.e. the tangent line, to approximate 1.6' as follows: x'. Find the equation of the tangent Let f(x) line to f(x) at x = 2 L(x) = Using this, we find our approximation for 1.6' is
Use linear approximation, i.e. the tangent line, to approximate 1.6' as follows: x'. Find the equation of the tangent Let f(x) line to f(x) at x = 2 L(x) = Using this, we find our approximation for 1.6' is
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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![**Title: Linear Approximation to Estimate Exponents**
**Objective:**
Use linear approximation, specifically the tangent line, to approximate \(1.6^7\).
**Instructions:**
1. **Define the Function:**
Let \( f(x) = x^7 \). Your task is to find the equation of the tangent line to \( f(x) \) at \( x = 2 \).
2. **Tangent Line Equation:**
Calculate the equation \( L(x) \) of the tangent line.
\( L(x) = \) *[Placeholder for tangent line equation]*
3. **Approximate the Value:**
Use the tangent line to find an approximation for \( 1.6^7 \).
The approximation for \( 1.6^7 \) is
*[Placeholder for approximation value]*
**Note:**
This exercise uses the concept of linear approximation to estimate the value of a function at a specific point using its tangent line. This method is useful in calculus for approximating values that are difficult to compute directly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb378457b-0f92-4bee-9968-071d7a742f72%2F05964056-a110-4a41-bccd-2eb5736d0f69%2Fc3luggr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Linear Approximation to Estimate Exponents**
**Objective:**
Use linear approximation, specifically the tangent line, to approximate \(1.6^7\).
**Instructions:**
1. **Define the Function:**
Let \( f(x) = x^7 \). Your task is to find the equation of the tangent line to \( f(x) \) at \( x = 2 \).
2. **Tangent Line Equation:**
Calculate the equation \( L(x) \) of the tangent line.
\( L(x) = \) *[Placeholder for tangent line equation]*
3. **Approximate the Value:**
Use the tangent line to find an approximation for \( 1.6^7 \).
The approximation for \( 1.6^7 \) is
*[Placeholder for approximation value]*
**Note:**
This exercise uses the concept of linear approximation to estimate the value of a function at a specific point using its tangent line. This method is useful in calculus for approximating values that are difficult to compute directly.
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