Answered: Determine wether the function f(x, y) =…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 58E

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Question

Determine wether the function f(x, y) = tan(x + y) is homogeneous, and if it is, determine its degree. A function f(x, y) is homogeneous of degree n if f(tx, ty) = tⁿf(x, y)

Expert Solution

Step 1

Given Data : Function $f (x, y) = \tan (x + y)$

To Find : Determine whether function is homogeneous or not and find the degree

The criteria for a function to be homogeneous is :

$f (z x, z y) = z^{n} f (x, y)$

Multiply each variable of the given function by z

$f (z x, z y) = \tan (z x + z y) f (z x, z y) = \frac{\tan z x + \tan z y}{1 - (\tan z x) (\tan z y)}$

$\frac{\tan z x + \tan z y}{1 - (\tan z x) (\tan z y)}$ cannot be express in the form of $z^{n} f (x, y)$

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