Question

Let A Rn and let f : A --> Rm. Write f = ( f1; f2;...

Let A Rn and let f : A --> Rm. Write f = ( f1; f2; f3; : : : ; fm) where f j = pj of f is

the jth coordinate function of f (note that pj : Rm -->R is the jth component function in Rm as

defined on p. 279 of Fitzpatrick). Let x* be a limit point of A and let L = (`1; `2; : : : ; `m) be an element of Rm.

Prove that lim x-->x* f (x) = L if and only if for each j = 1; : : : ;m, lim x-->x*f j(x) = l j.

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