Answered: determine if the limit exists

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determine if the limit exists

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Let a function g be defined on R² by g(x,y) = (x²ye^{sin(xy^2)})/(x²+y²)

use g(x,0), g(x,kx), g(x,kx²) , g(ly²,y), where k and l are constants (k =/ 0) and (l =/ 0), and g(rcosθ,rsinθ) to determine if lim_{(x,y)-->(0,0)}g(x,y) exists

Also use the squeeze technique to the determine if the limit exists

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