QUESTION 1

For 3x² - e^x = 0, Evaluate a function g and an interval [a; b] on which fixed-point iteration will converge to a positive solution of the equation.

QUESTION 2

Use Newton's method to solve the equation

with p₀ = Π/2

Iterate using Newton's method until an accuracy of 10^-5 is obtained.

QUESTION 3

The fourth-degree polynomial

has two real zeros, one in [-1,0] and the other in [0, 1]. Attempt to approximate these zeros to within 10 6 using the

a. Method of False Position

b. Secant method

c. Newton's method