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1. A function of two variables is given f(x, y) = x² + y² + e-(x² + y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f (x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?

1. A function of two variables is given f(x, y) = x² + y² + e-(x² + y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f (x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?

Advanced Engineering Mathematics
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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1. A function of two variables is given f(x, y) = x² + y² + e-(x²+y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f(x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?
Transcribed Image Text:1. A function of two variables is given f(x, y) = x² + y² + e-(x²+y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f(x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?
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