I am given with the function: $ f(x,y) = \frac{y\ln(1+x^2 + ay^2) } {x^2 + 2y^2} $ when $ (x,y)\neq (0,0)$, and $f(0,0)=0$ .
There is another given data; $ f_y (0,0) = 2 $ . What is the value of $a$ ?
I've tried computing the limit $ \frac{f(0,h)- f(0,0)}{h} $ , but it seems like it's always zero, contradicting the fact that $f_y(0,0)=2 $ !
Can someone help me understand my mistake?
Thanks !