For the given function, complete parts (a) through (f) below. f(x,y) = 4x² + 25y²

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Find the function's domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The domain is all points (x,y) satisfying
B. The domain is the entire xy-plane.
(Simplify your answer. Type an inequality.)
(b) Find the function's range. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The range is
OB. The range is all real numbers.
(c) Describe the function's level curves. Choose the correct answer below.
(Type your answer in interval notation.)
O A. For f(x,y) = 0, the level curve is the x- and y-axes. For f(x,y) ‡ 0, the level curves are hyperbolas with the x- and y-axes as asymptotes.
OB. The level curves are circles centered at the origin.
C. The level curves are parabolas of the form y = cx².
OD. For f(x,y) = 0, the level curve is the origin. For f(x,y) # 0, the level curves are ellipses centered at the origin and major and minor axes along the x- and y-axes, respectively.
Transcribed Image Text:(a) Find the function's domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is all points (x,y) satisfying B. The domain is the entire xy-plane. (Simplify your answer. Type an inequality.) (b) Find the function's range. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The range is OB. The range is all real numbers. (c) Describe the function's level curves. Choose the correct answer below. (Type your answer in interval notation.) O A. For f(x,y) = 0, the level curve is the x- and y-axes. For f(x,y) ‡ 0, the level curves are hyperbolas with the x- and y-axes as asymptotes. OB. The level curves are circles centered at the origin. C. The level curves are parabolas of the form y = cx². OD. For f(x,y) = 0, the level curve is the origin. For f(x,y) # 0, the level curves are ellipses centered at the origin and major and minor axes along the x- and y-axes, respectively.
For the given function, complete parts (a) through (f) below.
f(x,y) = 4x² +25y²
Transcribed Image Text:For the given function, complete parts (a) through (f) below. f(x,y) = 4x² +25y²
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