If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$? Thanks!
Equality is achieved when \(x^2 = y^2 = \frac{1}{2}\).
\(\max({|x|+|y|}) = \frac{\sqrt{2}}{2} \cdot 2 = \boxed{\sqrt{2}}\)
+1223 
