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+2 near the point (1,1,0). f(x, t)=sin(x- ct) near the point (7,2).

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Needed to be solved both question correctly in 1 hour and get the thumbs up These are very easy questions please solve both Q1&,Q2 in the order to get positive feedback must solve both I am repeating solve both take your time
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+x-y) at the point (0.01,-0.2) using local
linearization. Compare it with the value obtained by evaluating this function using a calculator.
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+x-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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