(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
Related questions
Question
Please review and solve problem 5 part 'a', 'b', 'c', 'd' and explain how the answer was found. Problem will be attached to this request.
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4effdf1a-67d0-42fb-b95c-7c4b54ad0624%2F46ea19dd-684f-479c-bfbc-131c34d40efe%2Fqxy8ii_processed.png&w=3840&q=75)
Transcribed Image Text:(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
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