# Limit of a multivariable function

#### hnnhcmmngs

1. Homework Statement

If possible, calculate the following limit:
$\lim_{(x,y)\rightarrow (0,0)} {\frac{2x^2 + 3y^2}{5xy}}$

2. Homework Equations

N/A

3. The Attempt at a Solution

I tried using both parametric and polar equations to find the limit, but neither worked. Setting either x or y equal to zero also won't work because of the denominator. What method should I use to solve this?

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#### scottdave

Homework Helper
Hello. The way that PhysicsForums works for homework problems: you provide what you have attempted, then we will guide you to a solution.
So what have you tried so far? Can you be more specific about the parametric and polar?

Homework Helper

#### Mark44

Mentor
Like @scottdave said...
The way that PhysicsForums works for homework problems: you provide what you have attempted, then we will guide you to a solution.
A technique that sometimes works is to take limits along various paths, such as along either axis or along a straight line through the origin or along various curves that pass through the origin. Finding the limit along various paths isn't enough to establish that a limit exists, but if you get different results along different paths, then you can say that the limit doesn't exist.

The fact that x and y occur to the same powers in both numerator and denominator makes things relatively easy in this problem.

#### WWGD

Gold Member
Somewhat-strangely, it is usually easier to show that the limit does not exist than to show it existr -- and find the limit.Specially -so in 2D or higher.

#### haruspex

Homework Helper
Gold Member
2018 Award
tried using ... polar equations
That should have solved it immediately. Please post your working. Maybe you did not understand what your equation was telling you.

#### scottdave

Homework Helper
So @hnnhcmmngs were you able to arrive at a conclusion on this limit?

"Limit of a multivariable function"

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