Recall that a polynomial of degree n is a function of the form P{x) =anxn + an-1 + + a1x +

Recall that a polynomial of degree n is a function of the form
P{x) =anxn + an-1 + ˆ™ ˆ™ ˆ™ ˆ™ + a1x + a0,
where aj ˆŠ R for j = 0,1,..., n and an ‰  0.
a) Prove that if 00 = 1, then limx†’a xn = an for n = 0,1, ˆ™ ˆ™ ˆ™ and a ˆŠ R.
b) Prove that if P is a polynomial, then

for every α ˆŠ R.

lina P(x) = P(a)