(5.) Consider the elliptic (circular) paraboloid f(x, y) = 2x² + 2(y − 1)². State the domain and range of f(x, y) (a. D= R R = {21220} (b. State the equation of the trace in the xz plane. y=0 => Z = 2x² + 2 (0-1) 2 (c. z = = 2+2x² Determine the value of k so that the level curve corresponding to f(x, y) = k gives a circle of radius 3 2 2х + 2(4-172 = k 2 + 2 (y-1)² = 152 K (+) = 9 (r²) 122 C=18 (d. Determine lim f(x, y) if it exists. If not, explain why. (x,y)→(2,2) Cont = F(2,2) = 2(2²) +2 (2-172 - 2(4)+2(1) === 8+2=10 = 10

(5.) Consider the elliptic (circular) paraboloid f(x, y) = 2x² + 2(y − 1)². State the domain and range of f(x, y) (a. D= R R = {21220} (b. State the equation of the trace in the xz plane. y=0 => Z = 2x² + 2 (0-1) 2 (c. z = = 2+2x² Determine the value of k so that the level curve corresponding to f(x, y) = k gives a circle of radius 3 2 2х + 2(4-172 = k 2 + 2 (y-1)² = 152 K (+) = 9 (r²) 122 C=18 (d. Determine lim f(x, y) if it exists. If not, explain why. (x,y)→(2,2) Cont = F(2,2) = 2(2²) +2 (2-172 - 2(4)+2(1) === 8+2=10 = 10

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 46E

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