How to compute such a limit? Knowing $f(x,y) = 2x^2 +3y^2 -7x +15y$,  one simply proves $$|f(x,y)|\leq 5(x^2+y^2)+22 \sqrt{x^2 + y^2}$$ How can I use this info to compute
$$ \lim_{(x,y)\to(0,0)} \frac{f(x,y) - 2(x^2+y^2)^{1/4}}{(x^2+y^2)^{1/4}}\;\;\; ?$$
Thanks!

Approach limit with $y = mx$
then 
$$
\lim_{(x,y)\to(0,0)} \frac{f(x,y) - 2(x^2+y^2)^{1/4}}{(x^2+y^2)^{1/4}} = 
$$
$$
\lim_{x\to0} \frac{x(2x +3m^2x -7 +15m)}{x^{1/2}(1+m^2)^{1/4}} - 2 = 
$$
$$
\lim_{x\to0} \frac{x^{1/2}( -7 +15m)}{(1+m^2)^{1/4}} - 2 = -2
$$
