   Chapter 14, Problem 10RE

Chapter
Section
Textbook Problem

Evaluate the limit or show that it does not exist.10. lim ( x , y ) → ( 0 , 0 ) 2 x y x 2 + 2 y 2

To determine

To find: The limit of the function lim(x,y)(0,0)(2xyx2+2y2) if exist, otherwise show that the limit does not exist.

Explanation

Result used:

“If f(x,y)L1 as (x,y)(a,b) along a path C1 and f(x,y)L2 as (x,y)(a,b) along a path C2 , where L1L2 , then lim(x,y)(a,b)f(x,y) does not exist”.

Calculation:

Consider the given function, lim(x,y)(0,0)(2xyx2+2y2) .

Let the path C1 be y=x and the path C2 be y=x2 .

Evaluate the limit (L1) along the curve y=x .

lim(x,y)(0,0)(2xyx2+2y2)=lim(x,y)(0,0)2x(x)x2+2(x)2=lim(x,y)(0,0)2x2x2+2x2=lim(x,y)(0,0)2x23x2=23

Thus, the limit along the curve y=x is L1=23

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find f'(a). f(x)=41x

Calculus: Early Transcendentals

Draw a polygon for the distribution of scores shown in the following table. X f 6 2 5 5 4 3 3 2 2 1

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integral. 12|ex1|dx

Calculus (MindTap Course List)

Evaluate limx1x31x1.

Single Variable Calculus

True or False: The function f is continuous at (0, 0), where

Study Guide for Stewart's Multivariable Calculus, 8th 