UNIVERSIDAD MAYOR DE SAN SIMÓN FACULTAD DE CIENCIAS Y TECNOLOGÍA CARRERA DE INGENIERÍA DE SISTEMAS PRACTICA I CÁLCULO NÚMERICO INTRODUCCIÓN AL CÁLCULO NÚMERICO DOCENTE: OSCAR ALBERTO ZABALAGA MONTAÑO MATERIA: CÁLCULO NÚMERICO CARRERA: INGENIERIA DE SISTEMAS ELABORADO POR: GUTIERREZ GONZALES JESUS ALESSANDRO PERIODO: 1-2021
EJERCICIO 1 Encontrar la distancia entre dos puntos p0(0.774976, 0.17631) y pN(0.968789, -0.847709) pertenecientes a la función ?2− ?2− 0.5??? mediante tres métodos: Método exacto mediante cálculo de integrales Método de las rectas tangentes Método de las rectas secantes Demostrar la desigualdad entre los métodos ????𝑝0−𝑝1≤ ?𝐸?𝑎??𝑎𝑝0−𝑝1≤ ??𝑎? 𝑝0−𝑝1 Método de las rectas secantes: Tomando puntos
Calculando la distancia punto a punto mediante rectas secantes obtendremos una distancia aproximada: ??? = √(0.689 − 0.774)2+ (−0.203 − 0.176)2= 0.389 ??? = √(0.791 − 0.689)2+ (−0.549 − (−0.203))2= 0.36 ??? = √(0.875 − 0.791)2+ (−0.705 − (−0.549))2 = 0.178 ??? = √(0.968 − 0.875)2+ (−0.847 − (−0.705))2 = 0.169 Por lo que la Distancia calculada por el método de las secantes será ????
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