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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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3.
a) Examine if the following limit exists,
If the limit exist, specify the value of the limit value. (
b) Is it possible to define f(0,1) such that f becomes continuous at the point (0,1) when
f(x,y)
=
x+y+1
lim
(x,y) (0,0) In(x2 + y²)*
x² + y²-1
x² + y² - 2y + 1
(Motivate your answer.) (1
for (x,y) (0,1)?

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In this example, we can combine the three simple results following the limit definition with the results in Theorem 1 to calculate the limits. We simply substitute the x- and y-values of the point being approached into the functional expression to find the limiting value.

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