1. Determine the root of the given equation x^2 - 3 = 0 for x ∈ [1, 2] using bisection method. S

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In this problem, we use bisection method. In first part, F of x is equal to 1 root x minus cos x

Question

1. Determine the root of the given equation $x^2 - 3 = 0$ for $x \in [1, 2]$ using bisection method. Show all the steps involved in the calculation and tabulate your results. Compare your findings using the quadratic formula. 2. (a) Show the steps to find the root for $f(x) = 2 - e^x$, and plot its graph for the interval $[-1, 1]$. (b) Do three iterations of Newton's method (by hand) for $f(x) = 2 - e^x$, $x_0 = 1$ for the interval $[0, 1]$. (c) Write a program using Python that uses Newton's method to find the root of the function, using $x_0$ as given. Stop the iteration when the error as estimated by $|x_{n+1} - x_n|$ is less than $10^{-6}$. (d) Repeat (c) but use the bisection method to find the root of the function, using the interval as given. (e) Repeat (d) but use the secant method using the interval as given. (f) Give an interpretation of your result using all three methods of the given function.

          1. Determine the root of the given equation $x^2 - 3 = 0$ for $x \in [1, 2]$ using bisection method. Show all the steps involved in the calculation and tabulate your results. Compare your findings using the quadratic formula.

2. (a) Show the steps to find the root for $f(x) = 2 - e^x$, and plot its graph for the interval $[-1, 1]$.
(b) Do three iterations of Newton's method (by hand) for $f(x) = 2 - e^x$, $x_0 = 1$ for the interval $[0, 1]$.
(c) Write a program using Python that uses Newton's method to find the root of the function, using $x_0$ as given. Stop the iteration when the error as estimated by $|x_{n+1} - x_n|$ is less than $10^{-6}$.
(d) Repeat (c) but use the bisection method to find the root of the function, using the interval as given.
(e) Repeat (d) but use the secant method using the interval as given.
(f) Give an interpretation of your result using all three methods of the given function.

1. Determine the root of the given equation x^2 - 3 = 0 for x ∈ [1, 2] using bisection method. Show all the steps involved in the calculation and tabulate your results. Compare your findings using the quadratic formula.

2. (a) Show the steps to find the root for f(x) = 2 - e^x, and plot its graph for the interval [-1, 1].
(b) Do three iterations of Newton's method (by hand) for f(x) = 2 - e^x, x0 = 1 for the interval [0, 1].
(c) Write a program using Python that uses Newton's method to find the root of the function, using x0 as given. Stop the iteration when the error as estimated by |xn+1 - xn| is less than 10^-6.
(d) Repeat (c) but use the bisection method to find the root of the function, using the interval as given.
(e) Repeat (d) but use the secant method using the interval as given.
(f) Give an interpretation of your result using all three methods of the given function.

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