(1) Describe the linear systems that are solved for the monomial basis, the Lagrange representation, and the Newton representation. (m) Describe the connection between the k th divided difference of a function f and its k th derivative. (n) Provide an expression for the error in polynomial interpolation as well as an error bound expression. (o) How does the smoothness of a function and its derivatives affect the quality of polynomial interpolants that approximate it, in general? (p) Give an example where the error bound is attained. (q) When we interpolate a function f given only data points, i.e., we do not know f or its derivatives, how can we gauge the accuracy of our approximation? (r) What are Chebyshev points and why are they important? (s) Describe osculating interpolation. How is it different from the usual polynomial interpolation? (t) What is a Hermite cubic interpolant