1. ## find limit

f(x,y)= (xy)/x^2+y^2

prove there is no value for f is continuous at (0,0).
they say I can use x=y => it will have 2 limit

but I don't know how to do it.

PlX Help...

2. What is the limit at $(0,0)$:
i) along the $x\text{-axis}?$
ii) along the line $y=x?$

3. Originally Posted by Plato
What is the limit at $(0,0)$:
i) along the $x\text{-axis}?$
ii) along the line $y=x?$

what do u mean along the x-axis
is it x=o?
then the function will become 1/y but the

4. Originally Posted by mathbeginner
what do u mean along the x-axis
is it x=o?
then the function will become 1/y but the
It helps to finish asking the question ....

You should have been taught how to tale limits along different paths. Along the x-axis, y = 0. Taking the limit x --> 0 your function clearly approaches 0.

Along the line y = x, you need to consider $\displaystyle \lim_{x \to 0} \frac{x^2}{x^2 + x^2}$.

Are these two limits the same? Draw a conclusion.

5. Along the line $y=x$ you have $\dfrac{x^2}{x^2+x^2}$.
So what is the limit?

6. thx a lot...
I think I make a careless mistake.