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Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation.

Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation.

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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Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation. O.
Transcribed Image Text:Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation. O.
Identify the traces. The horizontal trace at height c is a circle in the plane z = c for 0 < c < 1, The horizontal trace at height c is the origin in the plane z = c for c = 1. The vertical trace in the plane x = a is a parabola for all a. The vertical trace in the plane y = a is the curve z = x² + a² + 1 The vertical trace in the plane x = c is a circle for all c. Incorrect 口口 口 口
Transcribed Image Text:Identify the traces. The horizontal trace at height c is a circle in the plane z = c for 0 < c < 1, The horizontal trace at height c is the origin in the plane z = c for c = 1. The vertical trace in the plane x = a is a parabola for all a. The vertical trace in the plane y = a is the curve z = x² + a² + 1 The vertical trace in the plane x = c is a circle for all c. Incorrect 口口 口 口
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