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Let g1, g2: R2→ R be continuous. Define f: R2→Rby
f(x,y) =

(a) Show that D2f (x,y) = g2(x,y)

(b) How should f be defined so that D1f(x,y) =g1(x,y)?

(c) Find a function f: R2→R such that D1f (x,y)=x and D1f (x,y)=y

(a) Show that D2f (x,y) = g2(x,y)

(b) How should f be defined so that D1f(x,y) =g1(x,y)?

(c) Find a function f: R2→R such that D1f (x,y)=x and D1f (x,y)=y

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