What is the Limit of a Function in Two Variables at the Origin?

  • Thread starter Thread starter smatik
  • Start date Start date
  • Tags Tags
    Limit Variables
smatik
Messages
14
Reaction score
1

Homework Statement



lim (x,y)\rightarrow(0,0) f(x,y)=2*x/(x^{2} + x +y^{2})

Homework Equations



used different paths like y=k*x ,where k is a constant and y=k*x^2

The Attempt at a Solution


Got an answer 2 but solution says does not exist. Can anybody convince me that why limit does not exist,without using polar form.

I am currently studying in 1st year of college.
 
Physics news on Phys.org
The problem with the paths you chose is that there is one direction you are unable to represent with a finite k. What direction do you think that would be?
 
  • Like
Likes 1 person
oh got it thanks man. its the y axis! The limit comes out to be zero if i put x=1. Thanks!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Find limit of multi variable function
Replies
10
Views
1K
How to solve a limit in two variables with an indeterminate form at (0,0)?
Replies
35
Views
4K
Limit of a two-variable function
Replies
5
Views
1K
Determining domain for C^1 function
Replies
4
Views
1K
Limit problem involving two circles and a line
Replies
8
Views
1K
Real analysis: prove the limit exists
Replies
13
Views
3K
Two Limit exercises of functions of two variables.
Replies
1
Views
2K
Limit of a multivariable function
Replies
6
Views
2K
What is true for limit of f (x,y) as (x,y)→(0,1)?
Replies
3
Views
2K
Investigating Limit of Piecewise Function
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top