Find all exact roots of \(p\text{.}\) (Hint: \(p\) is divisible by \((3x-5)\)).
Plot \(p\) with MATLAB/Octave in the interval \([1.43,1.71]\text{.}\) (Hint: you can use x=linspace(1.43,1.71) together with the plot function).
What do you get via Newton's method with \(x_0=1.5\text{?}\) (Hint: replace the function and the initial point in our Newton code).
What do you get via the secant method with \(x_0=1\) and \(x_1=2\text{?}\) (Hint: replace the function and the initial points in our secant code).
What do you get via the bisection method applied to the interval \([1,2]\text{?}\) (Hint: replace the function and the interval endpoints in our bisection code)
2.
How many solutions does \(\tan x=x\) have? Find the smallest three positive roots with any of the three methods we learned. (Hint: plot the function and use Newton's method with suitable initial points).
3.
Use Newton's Method to estimate the value of \(\pi\) to ten decimal places. (Hint: choose any trigonometric equation having \(\pi\) as solution and choose an appropriate initial point).
