Problem Solving - Analysis
Problem Solving - Analysis M. Velrajan Understanding the problem, Mathematical thinking, Recalling all the results and examples related to the problem are essential to solve any problem in Mathematics. This way of problem solving is illustrated with 3 problems related to Analysis. 1. Let p be a real polynomial of the real variable x of the form p(x) = x n + a n-1 x n-1 + . . . + a 1 x -1. Suppose p has no root in the open unit disc and p(-1) = 0. Then (a) p(1) = 0 (b) lim x → ∞ p(x) = ∞ (c) p(2) > 0 (d) p(3) = 0 First look into what is given and then what has to be solved/found. Then recall whatever we know and that follow from the given, that are useful to proceed to solve. Here we are given p is a real monic polynomial of the real variable x with constant term - 1 and p has no root in the open unit disc. We have to find whether 1, 3 are roots of p, p(2) > 0 and lim x → ∞ p(x) = ∞ Think wh...