Register to reply 
Limits of functions of 2 variables 
Share this thread: 
#1
Oct2207, 09:01 PM

P: 93

1. The problem statement, all variables and given/known data
By considering different paths of approach, show that the function below has no limit as (x,y) > (0,0). f(x,y) =  x / sqrt(x^2 + y^2). 2. Relevant equations This is the problem! I do not know the different techniques to find the limits of functions of more than one variable. My book only shows examples of cases where you can get the answer by substituting y=mx or y=kx^2. 3. The attempt at a solution I tried the above substitutions but they don't work. 


#2
Oct2207, 10:05 PM

Sci Advisor
HW Helper
Thanks
P: 25,235

Why do you say y=mx doesn't work? You don't even get a limit for m=0.



#3
Oct2207, 10:32 PM

P: 93

When we substitute y=mx, we get 1/sqrt(1+m^2). So when m=0, the limit will be 1 won't it?



#4
Oct2207, 10:38 PM

Sci Advisor
HW Helper
Thanks
P: 25,235

Limits of functions of 2 variables
Depends on whether x is positive or negative. sqrt(x^2)=abs(x).



#5
Oct2207, 10:40 PM

P: 93

I didn't see that. Thanks!!



#6
Mar1208, 05:34 AM

P: 1

Hey. how do you solve:
lim(x,y)>(0,pi/2) ( x/cos(y) ) lots of thanks 


#7
Mar1208, 06:04 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,691

Have you noticed that these problems do NOT ask you to find the limit but to show that the limit does not exist? That is much simpler. Here, what limit do you get if you first let x go to 0, then let y go to [itex]\pi/2[/itex]? What limit do you get if you first let y go to [itex]\pi/2[/itex], then let x go to 0? What does that tell you?



Register to reply 
Related Discussions  
Limits in two variables  Calculus & Beyond Homework  22  
Limits of 2 variables  Calculus & Beyond Homework  1  
Functions of 3 Variables  Limits  Calculus & Beyond Homework  0  
Limits of Functions with several variables  Introductory Physics Homework  3  
Evaluating limits of several variables  Introductory Physics Homework  1 