Python

Problem 5 (6 points) [a] -Suppose that n! Pn(x) = (-1) -xk, -5 = 1, use a for-loop, vectorized, recursive approach. [b] Generate a plot showing Pn(x) for n = 0,1,2,3,4 on the same graph. Use different colors for each different n. You should provide a legend and labeled the axes. [c] Provide an expression for P.(x), P (x) and P2(x); this can be obtained by replacing n with 0, 1 and 2 respectively in Pn(x) above. Compare your expression for Po(x), P (x) and P2(x) with the graph you generate in part b above. Discuss if the graph is consistent with your expression for P.(x), P (x) and P2(x)