A polynomial on Rn of degree N is a function of the form where aj1 jn are scalars, N1,..., Nn are nonnegative integers, and N

A polynomial on Rn of degree N is a function of the form

where aj1 ˆ™ ˆ™ ˆ™ jn are scalars, N1,..., Nn are nonnegative integers, and N = N1 + N2 + ˆ™ ˆ™ ˆ™ + Nn. Prove that if P is a polynomial on Rn and a ˆˆ Rn, then limx†’a P(x) = P(a).

Na An)= ah .d.xt xh. p(xi , x2,