# Limits of functions of 2 variables

by mit_hacker
Tags: functions, limits, variables
 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.
 Sci Advisor HW Helper Thanks P: 25,167 Why do you say y=mx doesn't work? You don't even get a limit for m=0.
 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?
HW Helper
Thanks
P: 25,167

## Limits of functions of 2 variables

Depends on whether x is positive or negative. sqrt(x^2)=abs(x).
 P: 93 I didn't see that. Thanks!!
 P: 1 Hey. how do you solve: lim(x,y)-->(0,pi/2) ( x/cos(y) ) lots of thanks
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,879 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 $\pi/2$? What limit do you get if you first let y go to $\pi/2$, then let x go to 0? What does that tell you?

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