Let A be the set of the first 1000 odd natural numbers. Use Maple’s commands for set operations to determine how many elements in A are also triangular numbers or prime numbers.

Use Maple to find all quintic polynomials f(x) such that f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 6, f(5) = 10. Is there a cubic polynomial satisfying the conditions? If so, give this polynomial.

Use the bisection method in a while loop to estimate the root of f = (x − 1/9)(x − 2)(x − 3) which lies between 0 and 1 to an accuracy of 10^−4 .