Question 1

Find a root of the function f(x) = e^-x cos(x) starting with x₀ = 1.3 . The terminating conditions are given by ε_abs = 1e-5 and ε_step = 1e-5.

Answer: 1.57079632679490 after five iterations.

Question 2

Perform three steps of Newton's method for the function f(x) = x² - 2 starting with x₀ = 1. Use a calculator for the third step.

Answer: 3/2, 17/12, 577/408 ≈ 1.414215686274510