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.