Given the function f (x comma y) equalsStartFraction 1 Over StartRoot 36 minus 25 x squared minus 25 y squared EndRoot EndFraction , answer the following questions. a. Find the function's domain. b. Find the function's range. c. Describe the function's level curves. d. Find the boundary of the function's domain. e. Determine if the domain is an open region, a closed region, both, or neither. f. Decide if the domain is bounded or unbounded.

Question

Nikolai York

Mathematics

20 September, 14:19

Given the function f (x comma y) equalsStartFraction 1 Over StartRoot 36 minus 25 x squared minus 25 y squared EndRoot EndFraction , answer the following questions. a. Find the function's domain. b. Find the function's range. c. Describe the function's level curves. d. Find the boundary of the function's domain. e. Determine if the domain is an open region, a closed region, both, or neither. f. Decide if the domain is bounded or unbounded.

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Answers (1)

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Jimmy Collier · Answer 1

Step-by-step explanation:

f (x, y) = 1/√36 - 25x∧-2 - (25y²) ∧1/2

f (x, y) = 1/6 - 25x∧-2 - 5y

a) The relationship between x and y is said to be implicit

∴ differentiating term by term with respect to x

50x∧-3 - 5dy/dx = 0

5dy/dx = 50/x³

∴ dy/dx = 50/5x³ = 10/x³

b) No range

c) In absence of range, there is no function's level

d) No boundary

e) neither

f) unbounded