Answer:
This approach to (0,0) also gives the value 0
Step-by-step explanation:
Probably, you are trying to decide whether this limit exists or not. If you approach through the parabola y=x², you get
It does not matter if x>0 or x<0, the |x| on the denominator will cancel out with an x on the numerator, and you will get the term x²/(√(1+x²) which tends to 0.
If you want to prove that the limit doesn't exist, you have to approach through another curve and get a value different from zero.
However, in this case, the limit exists and its equal to zero. One way of doing this is to change to polar coordinates and doing a calculation similar to this one. Polar coordinates x=rcosФ, y=rsinФ work because the limit will only depend on r, no matter the approach curve.