MATH 157 Lecture Notes - Intermediate Value Theorem, Solution Process

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 157
• Professor: Stephen Choi

Document Summary

Instructor questions accompanying paper assignment # 6 solution. Directions: print double sided, write your solutions to both questions directly on this page, place immediately after cover page and staple together! Marks: an answer without a detailed solution process will be awarded zero marks! Q1: let f(x) = x4 5x3 + 8. Then: show that f(x) = 0 has a root between x = 1 and x = 2. Solution: since f(x) = x4 5x3 + 8, so f(cid:48)(x) = 4x3 15x2. The iterative formula is xn+1 = xn f(xn) f(cid:48)(xn) n 5x3 n + 8. 4x3 n n 15x3 n x4 n + 5x3 n(4xn 15) x2 n 8 n 10x3. Now take x0 = 1, we have x2 = 1. 363636364 x3 = 1. 294864839 x4 = 1. 292186672 x4 = 1. 292182581 . So an approximate root is x = 1. 2922. Solution: let y = 2x. then the equation becomes. Y 2 4y + 4 = 0.