ISyE 6644 — Summer 2020 — Test #3b Solutions (revised 7/22/20)

This test is 120 minutes. All questions are each worth 3 points. Let’s get some lawyer stuff out of the way. . . You’re allowed the following items: • Pencil / pen and scratch paper. • A reasonable calculator. • Three cheat sheets (6 sides total). • Normal, t, and χ2 tables. (I will supply these.) But note that • You are not allowed to use Arena, even though I’m asking questions about it. Good luck! I want you to make this test sorry that it ever tried to mess around with you!!! 1. Let’s use Newton’s method with x0 = 1 to find an approximate solution to x2 − 2 = 0. After 2 iterations, what is the approximate value of x2 ? Use 3 decimal places. (a) 1.410 (b) 1.417 (c) 1.448 (d) 1.500 (e) 1.514 Solution: Via Newton’s method: g(xn ) x2 n − 2 xn+1 ← xn − = x n − g 0 (xn ) 2xn Using x0 = 1: x20 − 2 12 − 2 1 x1 ← x0 − = 1 − = 2 + = 1.5, 2x0 2(1) 2