O uso de desigualdades na resolução de problemas

Abstract

Mathematical Inequalities, which are seldom addressed in primary and secondary education but can often be even more important than equality, are of utmost importance to many branches of mathematics, such as algebra, trigonometry, geometry and analysis, and constituem- is also very powerful tools for solving Olympiad problems, demonstration of geometric inequalities, maximum and minimum calculation and calculation limits. This work presents a clear and concise way some mathematical inequalities that do not need advanced studies in the area to be understood. A mind with some training for logical-mathematical reasoning, a brief knowledge of formal mathematics, algebra and plane geometry are fully aware su fi. Are presented is demonstrated: The Triangle Inequality, Inequality of Averages, Bernoulli's inequality, inequality Cauchy-Schwarz inequality of rearrangement, inequality Tchebishev, Jensen inequality, Young's inequality, Hölder's inequality, Minkowski inequality and the inequality Schur . At the end of the work, we take some of these inequalities to de fi ne the number of Euler and show the divergence of the harmonic series. We selected also some problems that students of basic education fi cam inhibited to solve them for not knowing such inequalities and only learn to solve with the knowledge Derivative when they arrive in higher education. Among them, lie questions of international Olympiads, optimization problems and how to find the equation of the line tangent to an ellipse through the inequality of Medium and Cauchy.