Define the norm in R 2
by ∥(x,y)∥=∣x∣+∣y∣( the 1 -norm). Let f:R 2
→R 2
be given by f(x,y)=( f 1
(x,y)
f 2
(x,y)
):=( 2xy
4x 2
+y 2
) Let Q={(x,y):∣x∣≤1,∣y∣≤2}. Show that f satisfies the Lipschitz condition on Q, i.e., there is a constant L>0 such that for any (x 1
,y )
,(x 2
,y 2
)∈Q, ∣f 1
(x 1
,y 1
)−f 1
(x 2
,y 2
)∣+∣f 2
(x 1
,y 1
)−f 2
(x 2
,y 2
)∣≤L(∣x 1
∣−x 2
∣+∣y 1
−y 2
∣) Also find an explicit Lipschitz constant L.