MAT 200, Logic, Language and Proof, Fall 2015 Practice Questions
... n consecutive integers all of which are composite. Hint : Consider (n + 1)! + 2, (n + 1)! + 3, . . . , (n + 1)! + n + 1. Problem 8. Prove that there are infinitely many prime numbers which are congruent to 3 modulo 4. Hint : Proceed as in the proof of Theorem 23.5.1, but consider m = ...
... n consecutive integers all of which are composite. Hint : Consider (n + 1)! + 2, (n + 1)! + 3, . . . , (n + 1)! + n + 1. Problem 8. Prove that there are infinitely many prime numbers which are congruent to 3 modulo 4. Hint : Proceed as in the proof of Theorem 23.5.1, but consider m = ...
4.2 Extreme Values Mon Dec 10
... • f '(x) is undefined at x = -3 however x = -3 is not included in the domain of f and cannot be a critical point. • The only criticalpoints of f are x = -7 and x = 1. ...
... • f '(x) is undefined at x = -3 however x = -3 is not included in the domain of f and cannot be a critical point. • The only criticalpoints of f are x = -7 and x = 1. ...
Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding ""best available"" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.