9. Let f(x, y) = 1+y a) Find the linearization L(x, y) of the function f at the point Po(1, 1). b) Find an upper bound of the error E in the approximation f(x, y) L(x, y) over the rectangle R: 0.9 ≤ x ≤ 1.1, 0.8 ≤ y ≤ 1.2. O =
9. Let f(x, y) = 1+y a) Find the linearization L(x, y) of the function f at the point Po(1, 1). b) Find an upper bound of the error E in the approximation f(x, y) L(x, y) over the rectangle R: 0.9 ≤ x ≤ 1.1, 0.8 ≤ y ≤ 1.2. O =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 9 please
![### Problem 9
#### Given Function:
\[ f(x, y) = \frac{4x}{1 + y} \]
#### Tasks:
a) Find the linearization \( L(x, y) \) of the function \( f \) at the point \( P_0(1, 1) \).
b) Find an upper bound of the error \( E \) in the approximation \( f(x, y) \approx L(x, y) \) over the rectangle \( R: 0.9 \leq x \leq 1.1, \; 0.8 \leq y \leq 1.2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb24b717-8ee5-4ca9-8061-74ddb7e91c1a%2Fc55290eb-0de3-4f6c-8655-13e5bd115349%2Fruar1h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 9
#### Given Function:
\[ f(x, y) = \frac{4x}{1 + y} \]
#### Tasks:
a) Find the linearization \( L(x, y) \) of the function \( f \) at the point \( P_0(1, 1) \).
b) Find an upper bound of the error \( E \) in the approximation \( f(x, y) \approx L(x, y) \) over the rectangle \( R: 0.9 \leq x \leq 1.1, \; 0.8 \leq y \leq 1.2 \).
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