lim of f(x,y)=frac{(x^{4}+4y^{2})}{(x^{2}+2y^{2})} at (0,0)

geduiwelh

geduiwelh

Answered question

2021-02-25

lim of f(x,y)=(x4+4y2)(x2+2y2) at (0,0)

Answer & Explanation

Alara Mccarthy

Alara Mccarthy

Skilled2021-02-26Added 85 answers

This limit does not exist. For instance, we can evaluate this limit along any linear path by substituting a general linear equation: y=mx where m∈R.
Now notice that x4+4y2x2+2y2=x2+4m21+2m24m21+2m2 as x0
What you notice from this is that you get a different limit value for each value of mm that you choose. In order for the limit to exist, we must have the same limiting value, no matter which path we take the limit on. Since this function give different limits for each linear equation, we can conclude that it doesn’t exist.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?