Let f(x, y) : and let L = lim( y)>(0,0) f(x, y). Which of the following 9x2 + 3y2 statements is correct? O L=0 O L=1/12 O L does not exist because f(x,y) is not defined at (0,0). O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from the one along the y-axis.

Let f(x, y) : and let L = lim( y)>(0,0) f(x, y). Which of the following 9x2 + 3y2 statements is correct? O L=0 O L=1/12 O L does not exist because f(x,y) is not defined at (0,0). O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from the one along the y-axis.

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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Concept explainers

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as:

Question

hx
Let f(x, y) =
and let L = lim2,y)>(0,0) f(x, y). Which of the following
%3D
9x2 + 3y2
statements is correct?
O L=0
O L=1/12
O L does not exist because f(x,y) is not defined at (0,0).
O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from
the one along the y-axis.
O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from
the one along the line x=y.
O L=3/8

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