Solution Recall that a function p is a polynomial function if it is defined by
p(x) = a0 + a1 x + + an xn for some natural number n, an ≠ 0 and ai ∈ R Clearly this
function is defined for every real number For a fixed real number c, we have
lim
( )
( )
x
c p x
p c
→
=
By definition, p is continuous at c