This exercise is used many places. Recall that a polynomial of degree n is a function of t...

This exercise is used many places. Recall that a polynomial of degree n is a function of the form

where a j ∈ R for j = 0, 1, . . . , n and an ≠ 0.

a) Prove that if 00 = 1, then limx→a xn = an for n = 0, 1, · · · and a ∈ R.

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b) Prove that if P is a polynomial, then

for every a ∈ R.