Recall that a polynomial of degree n is a function of the form P x) anxn an 1 a1x a0, where aj R for j 0,1, , n and an 0 a) Prove that if 00 1, then limxa xn an for n 0,1, and a R b) Prove that if P is a polynomial, then for every R lina P(x) P(a)...

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

Question:

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