Consider the function defined by f(r,y) and let (ro, yo) be a point on its domain. I - Y f(ro + h, yo) – f(ro, Yo) (a) Evaluate lim h→0 h (b) Use the result in item #3(a) to identify all points (x, y) E R? such that fa(x, y) exists. (c) Use differentiation theorems to find the partial derivative of f with respect to r.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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3. Consider the function defined by f(r, y) :
TY
and let (ro, Yo) be a point on its domain.
I - Y
f(To + h, yo) - f(To, yo)
(a) Evaluate lim
h→0
h
(b) Use the result in item #3(a) to identify all points (r, y) E R? such that fa(r, y) exists.
(c) Use differentiation theorems to find the partial derivative of f with respect to r.
Transcribed Image Text:3. Consider the function defined by f(r, y) : TY and let (ro, Yo) be a point on its domain. I - Y f(To + h, yo) - f(To, yo) (a) Evaluate lim h→0 h (b) Use the result in item #3(a) to identify all points (r, y) E R? such that fa(r, y) exists. (c) Use differentiation theorems to find the partial derivative of f with respect to r.
Expert Solution
Step 1

given

fx,y=xyx-y and let x0,y0 be a point on its domain

(a)

to evaluate 

limh0fx0+h,y0-fx0,y0h

substitute the value of function fx,y=xyx-y

 

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