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Consider f(x, y) = (x² + 2y²) a. Sketch cross sections (at least two) of f by keeping y fixed and then x fixed. b. Sketch a contour diagram for f with at least four labeled contours.

Consider f(x, y) = (x² + 2y²) a. Sketch cross sections (at least two) of f by keeping y fixed and then x fixed. b. Sketch a contour diagram for f with at least four labeled contours.

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. Consider f(x, y) = (x² + 2y²) a. Sketch cross sections (at least two) off by keeping y fixed and then x fixed. b. Sketch a contour diagram for f with at least four labeled contours. 2. Does the following table represent a linear function? Justify your answer. y 012 xo0 5 10 127 12 24914 3. Find the equation a linear function z = c + mx + ny whose graph contains the points (0,0,0), (0,2,-1) and (-3,0,-4). 4. Find a formula for a function f(x, y, z) whose level surface f = 1 is an ellipsoid (tri-axial) with center at (2,3,4) and the length in x, y, z axes are given by a, b, c respectively.
Transcribed Image Text:1. Consider f(x, y) = (x² + 2y²) a. Sketch cross sections (at least two) off by keeping y fixed and then x fixed. b. Sketch a contour diagram for f with at least four labeled contours. 2. Does the following table represent a linear function? Justify your answer. y 012 xo0 5 10 127 12 24914 3. Find the equation a linear function z = c + mx + ny whose graph contains the points (0,0,0), (0,2,-1) and (-3,0,-4). 4. Find a formula for a function f(x, y, z) whose level surface f = 1 is an ellipsoid (tri-axial) with center at (2,3,4) and the length in x, y, z axes are given by a, b, c respectively.
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