Finding Limit of Multivariable Function

[ultra100]

How do I go about finding the limit of a multivariable function? Example:

limit as (x,y) approach (0,0) of:

(x + 2y) / sqrt (x^2 + 4(y^2))



Do I need to use partial derivatives?

 

[jheld]

No. When dealing with multivariable limits you do not find their partial derivatives. Instead, you take a few instances and compare the results to each other. Such as x = 0, y = 0, x= y. If none of them match, then you can be certain that the limit does not exist.

 

[ultra100]

No. When dealing with multivariable limits you do not find their partial derivatives. Instead, you take a few instances and compare the results to each other. Such as x = 0, y = 0, x= y. If none of them match, then you can be certain that the limit does not exist.

What about when the numerator and denominator both go to 0, so you get 0/0?

I tried plugging in small numbers like 0.1 and 0.01 for x and y and i get 3/sqrt(5) as the answer, but my book says the limit does not exist for this equation

Is there a way to do L'Hospitals on multivariable limits?

 

[jheld]

No, unfortunately you can't use L'Hospitals for mutlivars. When both num and denom go to 0, that means that you need to substitute in y and x in different ways, like x = 0 in one case, and then y = 0 in another case, and then x = y in another. don't do them at the same time. don't plug in actual numbers (other than 0), only stuff like I noted above.