Question

Determine the positive real root of ln(x²)=0.7

(a) graphically,
(b) using three iterations of the bisection method, with initial guesses of x l​ =0.5 and x u =2, and
(c) using three iterations of the false-position method, with the same initial guesses as in (b)

Answer 1

To determine the positive real root of ln(x²)=0.7 (a) graphically, (b) using the bisection method, and (c) using the false-position method, follow these steps.

Step-by-step explanation:

To determine the positive real root of ln(x²)=0.7 (a) graphically, (b) using three iterations of the bisection method, and (c) using three iterations of the false-position method, follow these steps:

(a) Graphically: Plot the graph of y = ln(x²) and find the x-coordinate where y = 0.7.

(b) Bisection Method: Start with initial guesses of xl = 0.5 and xu = 2. Validate the initial guesses by checking if f(xl) and f(xu) have opposite signs. Apply the bisection method for three iterations to narrow down the interval where the positive real root exists.

(c) False-Position Method: Use the same initial guesses as in (b). Apply the false-position method for three iterations to approximate the positive real root.