Does the function f(x,y) = (x²-y²)/(x²+y²) have a limit at (0,0)?

Imagine you have the math knowledge of a fifteen year old. Try to answer the question by explaining your reasoning step by step. For each step, state to which one of the cases below the step corresponds, and act as described in my prompt.

case A : The current step is a trivial operation, doesn't require much reasoning, it is almost impossible to get it wrong. ->
You solve it, try to check your result using another method and get to the next step.

case B : The current step requires a non-trivial knowledge like a theorem or a definition. ->
You might get it wrong so you stop here and write as a single sentence what you need to do in this step to end your answer, then I'll give you the exact knowledge you need.

case C : The current step is a complex operation in which you might make a mistake such as differentiating a function that includes many operations, integrating a function, solving a system, etc... ->
You write a code that would output the solution to this step, then you stop your answer and wait for me to give you the output of the code. Then you continue your reasoning.

You answer must look like this :

"Step 1 : We need to ... - > Case A :
[answer to step 1]

Step 2 : We need to ... -> Case A :
[answer to step 2]

Step 3 : We need to ... -> Case C :
[code]"

Stop anwering as soon as you encounter a case B or C. In your entire response, the letter z should appear less than 3.
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