lim (x,y)->(0,0) (cosx-cosy)/(x-y)*(|x|+|y|)^(1/2)

[maxandri]

lim (x,y)->(0,0) (cosx-cosy)/(x-y)*(|x|+|y|)^1/2

itbecomes easily y^2-x^2 and it seems to go to 0 but it’s wrong.
Whichsubstitution I should do to understand how it goes?

 

[Prove It]

lim (x,y)->(0,0) (cosx-cosy)/(x-y)*(|x|+|y|)^1/2

itbecomes easily y^2-x^2 and it seems to go to 0 but it’s wrong.
Whichsubstitution I should do to understand how it goes?

As written it appears to be \(\displaystyle \displaystyle \begin{align*} \lim_{\left( x, y \right) \to \left( 0, 0 \right) } \left[ \frac{\cos{(x)} - \cos{(y)}}{x - y} \right] \left( \left| x \right| + \left| y \right| \right) ^{\frac{1}{2}} \end{align*}\), is that correct?