Problem $3(20$ points$)$

Consider the application of bisection algorithm to the function shown below. Initially, the algorithm is

started with lower and upper bounds given by $x_L=0$ and $x_{}=1\mathrm{.}0,$ respectively.

a$)(8$ points$)$ Fill out the table below with values of $x_L,x_R,$ and $x_U$ at each iteration. Note: it's advised

not to mark these points on the plot, in anticipation of part $($d$),$ and use the plot as a visual

reference instead.

b$)(3$ points$)$ After the completion of iteration $4,$ what is the value of the approximate percent

relative error, $E_a?$

c$)(3$ points$)$ After the completion of $4$ iterations, what is the value of the true percent relative

error, $E_t?$

d$)(6$ points$)$ As carefully as you can, use a graphical approach to show two iterations of the False$-$

Position method on the plot above. Circle the value of $x_R$ at the end of the two iterations.