# Thread: Need Help With Limits

1. ## Need Help With Limits

This is a true/false question, and I have to say why it's true or false:

lim (x,y)-->(0,0) |x^2 - y^2| / (x^2 + y^2) = 1

just in case it's hard to interpret the question, it says that the limit as (x,y) approaches (0,0) of |x^2 - y^2| / (x^2 + y^2) is equal to 1.

I'm not allowed to use L'Hospital's rule to explain this.

2. would it be enough to show that the function equals 0 along the line x=y and therefore prove the statement false?

This is a true/false question, and I have to say why it's true or false:

lim (x,y)-->(0,0) |x^2 - y^2| / (x^2 + y^2) = 1

just in case it's hard to interpret the question, it says that the limit as (x,y) approaches (0,0) of |x^2 - y^2| / (x^2 + y^2) is equal to 1.

I'm not allowed to use L'Hospital's rule to explain this.
It's helpful to note that $\displaystyle |x^2 + y^2| = x^2 + y^2$ for all real numbers. There will never be a time when $\displaystyle x^2 + y^2$ is negative for any real numbers.

Although I just realised that your expression is in fact $\displaystyle |x^2 - y^2 |$ so nevermind this!