1. Given a two variables function z = f(x, y) = √√√36 - 4x² — y². (i) Determine the domain and range of f. (ii) Sketch the contour of f (level curves of f projected on the xy-plane) for the values of z = 0, z = √11 and z = 6. (iii) Sketch the traces of f for (a) x = 0 and (b) y = 0. (iv) Sketch the surface of f in three dimensions. 2 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 43E
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1.
Given a two variables function z = f(x, y) = √√√36 - 4x² — y².
(i) Determine the domain and range of f.
(ii) Sketch the contour of f (level curves of f projected on the xy-plane) for the values
of z = 0, z = √11 and z = 6.
(iii) Sketch the traces of f for (a) x = 0 and (b) y = 0.
(iv) Sketch the surface of f in three dimensions.
2
2
Transcribed Image Text:1. Given a two variables function z = f(x, y) = √√√36 - 4x² — y². (i) Determine the domain and range of f. (ii) Sketch the contour of f (level curves of f projected on the xy-plane) for the values of z = 0, z = √11 and z = 6. (iii) Sketch the traces of f for (a) x = 0 and (b) y = 0. (iv) Sketch the surface of f in three dimensions. 2 2
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