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(c) h(x, y) = 1 In(9x² - y2)

(c) h(x, y) = 1 In(9x² - y2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the Domain and Range for c

(a) f(x, y) = √√y-x+1 (b) g(x, y) = ln(9-x² - y²) (c) h(x, y) = 1 In(9x² - y²)
Transcribed Image Text:(a) f(x, y) = √√y-x+1 (b) g(x, y) = ln(9-x² - y²) (c) h(x, y) = 1 In(9x² - y²)
Expert Solution
Step 1

c

Given that,

The function is hx,y=1ln9−x2−y2.

 

Domain:-

The domain is the set of input values for which the function is real and defined.

Here,

The function hx,y is defined where, 9−x2−y2>0

⇒−x2−y2>−9⇒x2+y2<9

Hence,

The domain of hx,y is x,y∈ℝ2:ln9−x2−y2≠0 and x2+y2<9.

And

The numerically estimated range is h∈ℝ: 0.45512≤h≤0.491709.

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