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(a) (b) x + y f(x, y) = √√x+y f(x, y) = sin (x+y) √√²-1

(a) (b) x + y f(x, y) = √√x+y f(x, y) = sin (x+y) √√²-1

Calculus: Early Transcendentals
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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find the domain

 

### Mathematical Functions #### Problem Set Consider the following functions of two variables, \(x\) and \(y\): **(a)** The function \(f(x, y)\) is defined as: \[ f(x, y) = \frac{x + y}{\sqrt{x + y}} \] **(b)** The function \(f(x, y)\) is given by: \[ f(x, y) = \frac{\sin(x + y)}{\sqrt{y^2 - 1}} \] ### Analysis - **Function (a):** The expression \(\frac{x + y}{\sqrt{x + y}}\) involves a rational function where the numerator is a linear expression \((x + y)\) and the denominator is the square root of this linear expression. - **Function (b):** The expression \(\frac{\sin(x + y)}{\sqrt{y^2 - 1}}\) combines trigonometric and algebraic aspects. The numerator is the sine of the sum of \(x\) and \(y\), while the denominator involves the square root of \(y^2 - 1\). These functions can be explored for their continuity, differentiability, and to study their behavior based on the values of \(x\) and \(y\).
Transcribed Image Text:### Mathematical Functions #### Problem Set Consider the following functions of two variables, \(x\) and \(y\): **(a)** The function \(f(x, y)\) is defined as: \[ f(x, y) = \frac{x + y}{\sqrt{x + y}} \] **(b)** The function \(f(x, y)\) is given by: \[ f(x, y) = \frac{\sin(x + y)}{\sqrt{y^2 - 1}} \] ### Analysis - **Function (a):** The expression \(\frac{x + y}{\sqrt{x + y}}\) involves a rational function where the numerator is a linear expression \((x + y)\) and the denominator is the square root of this linear expression. - **Function (b):** The expression \(\frac{\sin(x + y)}{\sqrt{y^2 - 1}}\) combines trigonometric and algebraic aspects. The numerator is the sine of the sum of \(x\) and \(y\), while the denominator involves the square root of \(y^2 - 1\). These functions can be explored for their continuity, differentiability, and to study their behavior based on the values of \(x\) and \(y\).
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