Limit of a multivariable function

[hnnhcmmngs]

Homework Statement

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

Homework Equations

N/A

The Attempt at a Solution

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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?

 

[scottdave]

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?

 

[scottdave]

I like Paul's Online Notes for Calculus problems. It may help you figure out if the limit exists, and what it's value is (if it exists).
http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx

 

[Mark44]

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]

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]

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]

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