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La forma más importante para impulsar el entendimiento es por medio de problemas que asignamos. Con ese fin se ha ideado varios tipos de problemas. Algunos conjuntos de ejercicios empiezan con peticiones para que el estudiante explique los significados de los conceptos básicos de la sección. Otros ejercicios prueban la comprensión de conceptos por medio de gráficas o tablas. Otro tipo de ejercicios usa descripción verbal para probar la comprensión de conceptos. La disponibilidad de tecnología no aminora la importancia de entender claramente los conceptos que sirven de base a las imágenes en pantalla, sino que la aumenta. Se utiliza como referencia en varios ejercicios el uso de un sistema computarizado de álgebra. (por ejemplo Derive, Maple o Mathematica). Maestros y estudiantes necesitan desarrollar su capacidad de determinar dónde es apropiado usar una máquina. En esta cuarta edición se destaca la comprensión conceptual por medio de métodos visuales, verbales, numéricos y algebraicos. Cuatro exámenes de diagnóstico han sido introducidos al principio del libro para diagnosticar el conocimiento de algebra básico, geometría analítica, funciones y trigonometría en el estudiante y de ser necesario en donde solicitar ayudar o reforzar los conceptos. Los ejemplos fueron titulados o nombrados para una mejor referencia, se agregaron nuevos ejemplos, algunas respuestas a ejercicios fueron detalladas más a fondo. Como parte de la retroalimentación recibida de ediciones anteriores algunos temas fueron reducidos en contenido, otro más fueron desarrollados con mayor profundidad.