Use Linear Approximation to estimate the change Af = f(a+Ax, b+ Ay) – f(a, b) in f when -0.1, Ay 0.2, and fæ(a, b) = 1, fy(a, b) = 3. 1. Af 2 0.5 2. Af 2 0.1 3. Af 0.2 4. Af 2 0.3 5. Af 2 0.4
Use Linear Approximation to estimate the change Af = f(a+Ax, b+ Ay) – f(a, b) in f when -0.1, Ay 0.2, and fæ(a, b) = 1, fy(a, b) = 3. 1. Af 2 0.5 2. Af 2 0.1 3. Af 0.2 4. Af 2 0.3 5. Af 2 0.4
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 Linear Approximation to Estimate Changes**
To estimate the change in a function \( f \), we use the formula:
\[
\Delta f = f(a + \Delta x, b + \Delta y) - f(a, b)
\]
Here, we are given:
\[
\Delta x = -0.1, \quad \Delta y = 0.2
\]
With the derivatives at the point \( (a, b) \):
\[
f_x(a, b) = 1, \quad f_y(a, b) = 3
\]
We aim to find \( \Delta f \) using the formula for linear approximation:
\[
\Delta f \approx f_x(a, b) \cdot \Delta x + f_y(a, b) \cdot \Delta y
\]
**Options for \( \Delta f \):**
1. \( \Delta f \approx 0.5 \)
2. \( \Delta f \approx 0.1 \)
3. \( \Delta f \approx 0.2 \)
4. \( \Delta f \approx 0.3 \)
5. \( \Delta f \approx 0.4 \)
The task is to calculate and choose the correct option for \( \Delta f \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F476a7a93-3242-4b81-b338-34642657d3b8%2Ff1cc0cb3-a498-4c7c-a17b-2af31760a754%2F4vfejf7_processed.png&w=3840&q=75)
Transcribed Image Text:**Using Linear Approximation to Estimate Changes**
To estimate the change in a function \( f \), we use the formula:
\[
\Delta f = f(a + \Delta x, b + \Delta y) - f(a, b)
\]
Here, we are given:
\[
\Delta x = -0.1, \quad \Delta y = 0.2
\]
With the derivatives at the point \( (a, b) \):
\[
f_x(a, b) = 1, \quad f_y(a, b) = 3
\]
We aim to find \( \Delta f \) using the formula for linear approximation:
\[
\Delta f \approx f_x(a, b) \cdot \Delta x + f_y(a, b) \cdot \Delta y
\]
**Options for \( \Delta f \):**
1. \( \Delta f \approx 0.5 \)
2. \( \Delta f \approx 0.1 \)
3. \( \Delta f \approx 0.2 \)
4. \( \Delta f \approx 0.3 \)
5. \( \Delta f \approx 0.4 \)
The task is to calculate and choose the correct option for \( \Delta f \).
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