Mathematics

Problem

Let

g:\mathbb R\to\mathbb R

be defined by

g(x)=3x^2-5x+1

. (a) Prove that

g

is continuous at the point

x=1

using the formal definition of continuity. Provide an explicit relationship between

\varepsilon

and

\delta

in your argument. (b) Use the structure of your proof in part (a) to explain why any polynomial is continuous at every real number.