Question: Consider the R2 R function given by f(x,y) = ( (x^2y^2)/(x^2+xy+2x+2y)) if x y and 0 if (x,y) = (0,0) or (x,y) = (2,2). (a)

Consider the R2 R function given by f(x,y) = ( (x^2y^2)/(x^2+xy+2x+2y)) if x y and 0 if (x,y) = (0,0) or (x,y) = (2,2).

(a) Write down the domain Df of f

(b) Determine lim (x,y)(0,0) f(x,y) and lim (x,y)(2,2) f(x,y).

(c) Calculate f(0,0) and f(2,2).

(d) Is f continuous at (x,y) = (0,0)?

(e) Is f continuous at (x,y) = (2,2)?

(f) Is f a continuous function?

Give reasons for your answers to (d), (e) and (f)

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