Answer the following questions about continuity of polynomial functions.
a. (i) Define continuity of a real-valued function at a point x=a.
b. (ii) Let p(x)=2x3−3x+1. Verify that p(x) is continuous at x=2 by applying the definition in part (i).
c. (iii) Using the result in part (ii) as a guide, prove that every polynomial function is continuous for all real numbers.