Question 1: What is the local linear approximation of the following functions near the point given? • f(x, y) = 4x² + 2y² - xy +5 near the point (0, 1) f(x, y, z)= near the point (1,1,0). • f(x, t) = sin(x- ct) near the point (7, 2).
Question 1: What is the local linear approximation of the following functions near the point given? • f(x, y) = 4x² + 2y² - xy +5 near the point (0, 1) f(x, y, z)= near the point (1,1,0). • f(x, t) = sin(x- ct) near the point (7, 2).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![1 Local linearization
Question 1: What is the local linear approximation of the following functions near the point given?
• f(x, y) = 4x² + 2y² - xy +5 near the point (0, 1)
• f(x, y, z) = ² near the point (1,1,0).
• f(x, t) = sin(x- ct) near the point (7,2).
Question 2: Provide an approximate value of f(x, y) = ln(1+z-y) at the point (0.01, -0.2) using local
linearization. Compare it with the value obtained by evaluating this function using a calculator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e7f1ffc-9b2b-42b3-8d28-d686ec9f0103%2Fe63d25ef-5db0-4443-bf42-4a3e82f5b1e8%2Ffjn4y4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 Local linearization
Question 1: What is the local linear approximation of the following functions near the point given?
• f(x, y) = 4x² + 2y² - xy +5 near the point (0, 1)
• f(x, y, z) = ² near the point (1,1,0).
• f(x, t) = sin(x- ct) near the point (7,2).
Question 2: Provide an approximate value of f(x, y) = ln(1+z-y) at the point (0.01, -0.2) using local
linearization. Compare it with the value obtained by evaluating this function using a calculator.
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